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We investigate the effects of interfacial spin-orbit coupling (ISOC) on superconductors, focusing on its impact on electronic transport and spin-charge conversion. Using a symmetry-based nonlinear sigma model, we derive effective boundary conditions for the Usadel and Maxwell equations that account for spin-galvanic effect, spin relaxation, and spin precession. This approach allows for the analysis of various interfaces without relying on specific microscopic models. We apply these boundary conditions to derive ISOC-induced terms in the Ginzburg-Landau functional, which is then used to compute the critical temperature of superconducting films with ISOC subjected to an external magnetic field. Our findings show that, contrary to a recent prediction, the critical temperature of a film cannot be enhanced by an external magnetic field. Additionally, we demonstrate that the combination of ISOC and an external magnetic field leads to a superconducting diode effect. Its efficiency strongly depends on the interplay between the spin-galvanic and the spin relaxation terms. Our results provide a framework for understanding ISOC in superconducting systems and highlight the potential for optimizing diode efficiency through careful interface engineering, Comment: 20 pages, 3 figures

We propose a macroscopic theory of optical phonons, Fr{\"oh}lich polarons, and exciton-polarons in two-dimensional (2D) polar crystalline monolayers. Our theory extends the classical macroscopic formulation of the electron-phonon problem in three-dimensional (3D) polar crystals to the new generation of 2D materials. Similarly to the 3D case, in our approach, the effective electron-phonon Hamiltonian is parametrized solely in terms of macroscopic experimentally accessible quantities -- 2D polarizabilities of the monolayer at low and high frequencies. We derive the dispersion of long wave length longitudinal optical (LO) phonons, which can be viewed as a 2D form of the Lyddane-Sachs-Teller relation, and study the formation of 2D Fr{\"oh}lich polarons by adopting the intermediate coupling approximation. Finally, we apply this approach to excitons in polar 2D crystals and derive an effective potential of the electron-hole interaction dressed by LO phonons. Due to the specific dispersion of LO phonons, the polarons and exciton-polarons in 2D materials exhibit unique features not found in their 3D counterparts. As an illustration, the polaron and exciton-polaron binding energies are computed for a representative set of 2D polar crystals, demonstrating the interplay between dimensionality, polarizability of materials, and electron-phonon coupling.

We formulate and analyze in detail the ground state quantum electrodynamical density functional theory (QEDFT) for a generalized Dicke model describing a collection of $N$ tight-binding dimers minimally coupled to a cavity photon mode. This model is aimed at capturing essential physics of molecules in quantum cavities in polaritonic chemistry, or quantum emitters embedded in mesoscopic resonators of the circuit QED, and, because of its simplicity, is expected to provide important insights regarding the general QEDFT. We adopt the adiabatic connection formalism and the diagrammatic many-body theory to regularly derive a sequence of explicit approximations for the exchange-correlation (xc) energy in the ground state QEDFT, and to compare their performance with the results of exact numerical diagonalization. Specifically, we analyze the earlier proposed one-photon optimized effective potential (OEP) scheme, its direct second order extensions, and a non-perturbative xc functional based on the photon random phase approximation (RPA). Our results demonstrate the excellent performance of RPA-QEDFT in the ultrastrong coupling regime, and for any number $N$ of Dicke molecules in the cavity. We study in detail the scaling of xc energy with $N$, and emphasize the importance for the ground state QEDFT of collective effects in the interaction of molecules with cavity photons. Finally, we discuss implications of our results for realistic systems.

Conventional superconductors naturally disfavor ferromagnetism because the supercurrent-carrying electrons are paired into anti-parallel spin singlets. In superconductors with strong Rashba spin-orbit coupling, impurity magnetic moments induce supercurrents through the spin-galvanic effect. As a result, long-range ferromagnetic interaction among the impurity moments may be mediated through such anomalous supercurrents in a similar fashion as in itinerant ferromagnets. Fe(Se,Te) is such a superconductor with topological surface bands, previously shown to exhibit quantum anomalous vortices around impurity spins. Here, we take advantage of the flux sensitivity of scanning superconducting quantum interference devices to investigate superconducting Fe(Se,Te) in the regime where supercurrents around impurities overlap. We find homogeneous remanent flux patterns after applying a supercurrent through the sample. The patterns are consistent with anomalous edge and bulk supercurrents generated by in-plane magnetization, which occur above a current threshold and follow hysteresis loops reminiscent of those of a ferromagnet. Similar long-range magnetic orders can be generated by Meissner current under a small out-of-plane magnetic field. The magnetization weakens with increasing temperature and disappears after thermal cycling to above superconducting critical temperature; further suggesting superconductivity is central to establishing and maintaining the magnetic order. These observations demonstrate surface anomalous supercurrents as a mediator for ferromagnetism in a spin-orbit coupled superconductor, which may potentially be utilized for low-power cryogenic memory.

We investigate the behavior of magnetic impurities placed on the surface of superconductor thin films with spin-orbit coupling. Our study reveals long-range interactions between the impurities, which decay according to a power law, mediated by the supercurrents. Importantly, these interactions possess a ferromagnetic component when considering the influence of the electromagnetic field, leading to the parallel alignment of the magnetic moments in the case of two impurities. In a Bravais lattice of magnetic impurities, superconductivity facilitates the establishment of ferromagnetic order within specific parameter ranges. These findings challenge the conventional understanding that ferromagnetism and superconductivity are mutually exclusive phenomena. Our theoretical framework provides a plausible explanation for the recently observed remanent flux in iron-based superconductors, particularly Fe(Se,Te)., Comment: 5 pages, 3 figures + supplmentary material (5 pages)

Motivated by recent discoveries of superconductivity in lightly-doped multilayer graphene systems, we present a low-energy model to study superconductivity in 2D materials whose Fermi surface consists of two valleys at $\pm \vec{K}$-points. We assume a triplet odd-valley superconducting order with a pair potential that is isotropic in each valley but has a different sign in the two different valleys. Our theory predicts the emergence of an almost flat band of edge states centered at zero energy for certain edge orientations. As a result, a prominent experimental signature of this type of superconductivity is the presence of a large zero-energy peak in the local density of states near specific edges. The results of the effective low-energy theory are confirmed by numerically analyzing a specific microscopic tight-binding realization of odd-valley superconductivity, f-wave superconductivity on a honeycomb lattice in a ribbon geometry. Our work provides a test for odd-valley superconductivity through edge spectroscopy., Comment: 4 pages, 3 figures

We show that the analytic structure of the dynamical xc kernels of semiconductors and insulators can be sensed in terms of its poles which mark physically relevant frequencies of the system where the counter-phase motion of discrete collective excitations occurs: if excited, the collective modes counterbalance each other, making the system to exhibit none at all or extremely weak density response. This property can be employed to construct simple and practically relevant approximations of the dynamical xc kernel for time-dependent density functional theory (TDDFT). Such kernels have simple analytic structure, are able to reproduce dominant excitonic features of the absorption spectra of monolayer semiconductors and bulk solids, and promise high potential for future uses in efficient real-time calculations with TDDFT., Comment: 10 pages, 4 figures

We developed a theory of electron scattering by a short-range repulsive potential in a cavity. In the regime of ultrastrong electron coupling to the cavity electromagnetic field, the vacuum fluctuations of the field result in the dynamical stabilization of a quasistationary polariton state confined in the core of the repulsive potential. When the energy of a free electron coincides with the energy of the confined state, the extremely efficient resonant nonelastic scattering of the electron accompanied by emission of a cavity photon appears. This effect is discussed as a basis for possible free-electron sources of nonclassical light., Comment: Published version

We derive the nonlinear $\sigma$-model to describe diffusive transport in normal metals and superconductors with intrinsic spin-orbit coupling (SOC). The SOC is described via an SU(2) gauge field, and we expand the model to the fourth order in gradients to find the leading non-Abelian field-strength contribution. This contribution generates the spin-charge coupling that is responsible for the spin-Hall effect. We discuss how its symmetry differs from the leading quasiclassical higher-order gradient terms. We also derive the corresponding Usadel equation describing the diffusive spin-charge dynamics in superconducting systems. As an example, we apply the obtained equations to describe the anomalous supercurrent in dirty Rashba superconductors at arbitrary temperatures., Comment: 13 pages + supplementary material

We generalize the optimized effective potential (OEP) formalism in the quantum electrodynamical density functional theory (QEDFT) to the case of continuous distribution of photon modes, and study its applicability to dissipative dynamics of electron systems interacting with photons of lossy cavities. Specifically, we test whether this technique is capable of capturing the quantum features of electron-photon interaction related to spontaneous emission and the corresponding energy transfer from the electrons to cavity photons. For this purpose, we analyze a discrete three-site system with one electron coupled to photons of the cavity, which, in fact, is a minimal model allowing to eliminate classical radiation and the corresponding energy loss, but still have nontrivial density dynamics. By considering two typical spectral densities of photon modes, modeling (i) lossy cavity with Lorentzian broadening of photon peaks, and (ii) the Ohmic bath, and several representative dynamical regimes, we find that OEP-QEDFT demonstrates a good qualitative and quantitative performance, especially in the case when the disspation is dominated by one-photon processes.

We suggest a generalization of nonlinear $\sigma$-model for diffusive superconducting systems to account for magnetoelectric effects due to spin-orbit scattering. In the leading orders of spin-orbit strength and gradient expansion it includes two additional terms responsible for the spin-Hall effect and the spin-current swapping. First, assuming a delta-correlated disorder we derive the new terms from the Keldysh path integral representation of the generating functional. Then we argue phenomenologically that they exhaust all invariants allowed in the effective action to the leading order in the spin-orbit coupling (SOC). Finally, the results are confirmed by a direct derivation of the saddle-point (Usadel) equation from the quantum kinetic equations in the presence of randomly distributed impurities with SOC. At this point we correct a recent derivation of the Usadel equation that includes magneto-electric effects and does not resort to the Born approximation., Comment: 6 pages

We study a periodic arrangement of magnetic regions in a one-dimensional superconducting wire. Due to the local exchange field, each region supports Andreev bound states that hybridize forming Bloch bands in the subgap spectrum of what we call the Andreev crystal (AC). As an illustration, ACs with ferromagnetic and antiferromagnetic alignment of the magnetic regions are considered. We relate the spectral asymmetry index of a spin-resolved Hamiltonian to the spin polarization and identify it as the observable that quantifies the closing and reopening of the excitation gap. In particular, antiferromagnetic ACs exhibit a sequence of gapped phases separated by gapless Dirac phase boundaries. Heterojunctions between antiferromagnetic ACs in neighboring phases support spin-polarized bound states at the interface. In a close analogy to the charge fractionalization in Dirac systems with a mass inversion, we find a fractionalization of the interface spin., Comment: 6 pages, 4 figures

A battery is a classical apparatus which converts a chemical reaction into a persistent voltage bias able to power electronic circuits. Similarly, a phase battery is a quantum equipment which provides a persistent phase bias to the wave function of a quantum circuit. It represents a key element for quantum technologies based on quantum coherence. Unlike the voltage batteries, a phase battery has not been implemented so far, mainly because of the natural rigidity of the quantum phase that, in typical quantum circuits, is imposed by the parity and time-reversal symmetry constrains. Here we report on the first experimental realization of a phase battery in a hybrid superconducting circuit. It consists of an n-doped InAs nanowire with unpaired-spin surface states and proximitized by Al superconducting leads. We find that the ferromagnetic polarization of the unpaired-spin states is efficiently converted into a persistent phase bias $\varphi_0$ across the wire, leading to the anomalous Josephson effect. By applying an external in-plane magnetic field a continuous tuning of $\varphi_0$ is achieved. This allows the charging and discharging of the quantum phase battery and reveals the symmetries of the anomalous Josephson effect predicted by our theoretical model. Our results demonstrate how the combined action of spin-orbit coupling and exchange interaction breaks the phase rigidity of the system inducing a strong coupling between charge, spin and superconducting phase. This interplay opens avenues for topological quantum technologies, superconducting circuitry and advanced schemes of circuit quantum electrodynamics.}, Comment: 6 pages, 3 figures and Supplementary Material

We demonstrate that the interplay of Zeeman and spin-orbit coupling fields in a 1D wire leads to an equilibrium spin current that manifests itself in a spin accumulation at the wire ends with a polarization perpendicular to both fields. This is a universal property that occurs in the normal and superconducting state independently of the degree of disorder. We find that the edge spin polarization transverse to the Zeeman field is strongly enhanced in the superconducting state when the Zeeman energy is of the order of the superconducting gap. By calculating the space resolved magnetization response of the wire we demonstrate that the transverse component of the spin at the wire edges can be much larger than the one parallel to the field. This result generalizes the well established theory of the Knight-shift in superconductors to the case of finite systems., Comment: 5 pages, 4 figures

By analyzing the many-body problem for non-relativistic electrons strongly coupled to photon modes of a microcavity I derive the exact momentum/force balance equation for cavity quantum electrodynamics. Implications of this equation for the electron self-energy and the exchange-correlation potential of quantum electrodynamic time-dependent density functional (QED-TDDFT) are discussed. In particular I generalize the concept of $\Phi$-derivability to construct approximations which ensure the correct momentum balance. It is shown that a recently proposed optimized effective potential approximation for QED-TDDFT is conserving and its possible improvements are discussed., Comment: 9 pages, 1 figure

The Usadel equation is the standard theoretical tool for the description of superconducting structures in the diffusive limit. Here I derive the Usadel equation for gyrotropic materials with a generic linear in momentum spin-orbit coupling. It accounts for the spin-charge/singlet-triplet coupling and in the normal state reduces to the system of spin-charge diffusion equations describing various magneto-electric effects, such as the spin Hall effect (SHE), the spin-galvanic effect (SGE) and their inverses. Therefore the derived Usadel equation establishes a direct connection of these effects to their superconducting counterparts. The working power of the present formalism is illustrated on the example of the bulk SGE., Comment: 5 pages

We demonstrate that in diffusive superconductor/ferromagnet/superconductor (S/F/S) junctions a finite, {\it anomalous}, Josephson current can flow even at zero phase difference between the S electrodes. The conditions for the observation of this effect are non-coplanar magnetization distribution and a broken magnetization inversion symmetry of the superconducting current. The latter symmetry is intrinsic for the widely used quasiclassical approximation and prevent previous works, based on this approximation, from obtaining the Josephson anomalous current. We show that this symmetry can be removed by introducing spin-dependent boundary conditions for the quasiclassical equations at the superconducting/ferromagnet interfaces in diffusive systems. Using this recipe we considered generic multilayer magnetic systems and determine the ideal experimental conditions in order to maximize the anomalous current., Comment: In this version the references are updated

We present a comprehensive quasiclassical approach for studying transport properties of superconducting diffusive hybrid structures in the presence of extrinsic spin-orbit coupling. We derive a generalized Usadel equation and boundary conditions that in the normal state reduce to the drift-diffusion theory governing the spin-Hall effect in inversion symmetric materials. These equations predict the non-dissipative spin-galvanic effect, that is the generation of supercurrents by a spin-splitting field, and its inverse -- the creation of magnetic moment by a supercurrent. These effects can be seen as counterparts of the spin-Hall, anomalous Hall and their inverse effects in the superconducting state. Our theory opens numerous possibilities for using superconducting structures in magnetoelectronics., Comment: 10 pages, 2 figures

We consider response function and spin evolution in spin-orbit coupled cold atomic gases in a synthetic gauge magnetic field influencing solely the orbital motion of atoms. We demonstrate that various regimes of spin-orbit coupling strength, magnetic field, and disorder can be treated within a single approach based on the representation of atomic motion in terms of auxiliary collective classical trajectories. Our approach allows for a unified description of fermionic and bosonic gases., Comment: 8 pages, 2 figures

We use analytic (current) density-potential maps of time-dependent (current) density functional theory (TD(C)DFT) to inverse engineer analytically solvable time-dependent quantum problems. In this approach the driving potential (the control signal) and the corresponding solution of the Schr\"odinger equation are parametrized analytically in terms of the basic TD(C)DFT observables. We describe the general reconstruction strategy and illustrate it with a number of explicit examples. First we consider the real space one-particle dynamics driven by a time-dependent electromagnetic field and recover, from the general TDDFT reconstruction formulas, the known exact solution for a driven oscillator with a time-dependent frequency. Then we use analytic maps of the lattice TD(C)DFT to control quantum dynamics in a discrete space. As a first example we construct a time-dependent potential which generates prescribed dynamics on a tight-binding chain. Then our method is applied to the dynamics of spin-1/2 driven by a time dependent magnetic field. We design an analytic control pulse that transfers the system from the ground to excited state and vice versa. This pulse generates the spin flip thus operating as a quantum NOT gate., Comment: 11 pages, 6 figures

It is well known that a current driven through a two-dimensional electron gas with Rashba spin-orbit coupling induces a spin polarization in the perpendicular direction (Edelstein effect). This phenomenon has been extensively studied in the linear response regime, i.e., when the average drift velocity of the electrons is a small fraction of the Fermi velocity. Here we investigate the phenomenon in the nonlinear regime, meaning that the average drift velocity is comparable to, or exceeds the Fermi velocity. This regime is realized when the electric field is very large, or when electron-impurity scattering is very weak. The quantum kinetic equation for the density matrix of noninteracting electrons is exactly and analytically solvable, reducing to a problem of spin dynamics for "unpaired" electrons near the Fermi surface. The crucial parameter is $\gamma=eEL_s/E_F$, where $E$ is the electric field, $e$ is the absolute value of the electron charge, $E_F$ is the Fermi energy, and $L_s = \hbar/(2m\alpha)$ is the spin-precession length in the Rashba spin-orbit field with coupling strength $\alpha$. If $\gamma\ll1$ the evolution of the spin is adiabatic, resulting in a spin polarization that grows monotonically in time and eventually saturates at the maximum value $n(\alpha/v_F)$, where $n$ is the electron density and $v_F$ is the Fermi velocity. If $\gamma \gg 1$ the evolution of the spin becomes strongly non-adiabatic and the spin polarization is progressively reduced, and eventually suppressed for $\gamma\to \infty$. We also predict an inverse nonlinear Edelstein effect, in which an electric current is driven by a magnetic field that grows linearly in time. The "conductivities" for the direct and the inverse effect satisfy generalized Onsager reciprocity relations, which reduce to the standard ones in the linear response regime., Comment: 21 pages, 7 figures

The broken inversion symmetry at the surface of a metallic film (or, more generally, at the interface between a metallic film and a different metallic or insulating material) greatly amplifies the influence of the spin-orbit interaction on the surface properties. The best known manifestation of this effect is the momentum-dependent splitting of the surface state energies (Rashba effect). Here we show that the same interaction also generates a spin-polarization of the bulk states when an electric current is driven through the bulk of the film. For a semi-infinite jellium model, which is representative of metals with a closed Fermi surface, we prove as a theorem that, regardless of the shape of the confinement potential, the induced surface spin density at each surface is given by ${\bf S} =-\gamma \hbar {\bf \hat z}\times {\bf j}$, where ${\bf j}$ is the particle current density in the bulk, ${\bf \hat z}$ the unit vector normal to the surface, and $\gamma=\frac{\hbar}{4mc^2}$ contains only fundamental constants. For a general metallic solid $\gamma$ becomes a material-specific parameter that controls the strength of the interfacial spin-orbit coupling. Our theorem, combined with an {\it ab initio} calculation of the spin polarization of the current-carrying film, enables a determination of $\gamma$, which should be useful in modeling the spin-dependent scattering of quasiparticles at the interface., Comment: 5 pages, 2 figures

We present a full microscopic theory based on the SU(2) covariant formulation of the quasiclassical formalism to describe the Josephson current through an extended superconductor-normal metal- superconductor (SNS) diffusive junction with an intrinsic spin-orbit coupling (SOC) in the presence of a spin-splitting field h. We demonstrate that the ground state of the junction corresponds to a finite intrinsic phase difference 0 < {\phi}0 < 2{\pi} between the superconductor electrodes provided that both, h and the SOC-induced SU(2) Lorentz force are finite. In the particular case of a Rashba SOC we present analytic and numerical results for {\phi}0 as a function of the strengths of the spin fields, the length of the junction, the temperature and the properties of SN interfaces., Comment: 5 pages, 2 figures

We present a rigorous formulation of the time-dependent density functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic mode, which is equivalent to the single mode spin-boson model or the quantum Rabi model. For this system we prove that the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate, provided the initial state and the density satisfy a set of well defined conditions. Then we generalize the formalism to many interacting electrons on a lattice coupled to multiple photonic modes and prove the general mapping theorem. We also show that for a system evolving from the ground state of a lattice Hamiltonian any density with a continuous second time derivative is locally $v$-representable., Comment: 9 pages, 1 figure

We investigate the proximity effect in diffusive superconducting hybrid structures with a spin-orbit (SO) coupling. Our study is focused on the singlet-triplet conversion and the generation of long-range superconducting correlations in ferromagnetic elements. We derive the quasiclassical equations for the Green's functions including the SO coupling terms in form of a background SU(2) field. With the help of these equations, we first present a complete analogy between the spin diffusion process in normal metals and the generation of the triplet components of the condensate in a diffusive superconducting structure in the presence of SO coupling. From this analogy it turns out naturally that the SO coupling is an additional source of the long-range triplet component (LRTC) besides the magnetic inhomogeneities studied in the past. We demonstrate an explicit connection between an inhomogeneous exchange field and SO coupling mechanisms for the generation of the LRTC and establish the conditions for the appearance of the LRTC in different geometries. We also consider a S/F bilayer in contact with normal metal with SO coupling and show that the latter can be used as a source for the LRTC. Our work gives a global description of the singlet-triplet conversion in hybrids structures in terms of generic spin-fields and our results are particularly important for the understanding of the physics underlying spintronics devices with superconductor elements.

Time-dependent (current) density functional theory for many-electron systems strongly coupled to quantized electromagnetic modes of a microcavity is proposed. It is shown that the electron-photon wave function is a unique functional of the electronic (current) density and the expectation values of photonic coordinates. The Kohn-Sham system is constructed, which allows to calculate the above basic variables by solving selfconsistent equations for noninteracting particles. We suggest possible approximations for the exchange-correlation potentials and discuss implications of this approach for the theory of open quantum systems., Comment: 4+ pages

We consider spin relaxation dynamics in cold Fermi gases with a pure-gauge spin-orbit coupling corresponding to recent experiments. We show that such experiments can give a direct access to the collisional spin drag rate, and establish conditions for the observation of spin drag effects. In the recent experiments the dynamics is found to be mainly ballistic leading to new regimes of reversible spin relaxation-like processes., Comment: 5 pages, 2 figures

The derivative discontinuity of the exchange-correlation (xc) energy at integer particle number is a property of the exact, unknown xc functional of density functional theory (DFT) which is absent in many popular local and semilocal approximations. In lattice DFT, approximations exist which exhibit a discontinuity in the xc potential at half filling. However, due to convergence problems of the Kohn-Sham (KS) self-consistency cycle, the use of these functionals is mostly restricted to situations where the local density is away from half filling. Here a numerical scheme for the self-consistent solution of the lattice KS Hamiltonian with a local xc potential with rapid (or quasi-discontinuous) density dependence is suggested. The problem is formulated in terms of finite-temperature DFT where the discontinuity in the xc potential emerges naturally in the limit of zero temperature. A simple parametrization is suggested for the xc potential of the uniform 1D Hubbard model at finite temperature which is obtained from the solution of the thermodynamic Bethe ansatz. The feasibility of the numerical scheme is demonstrated by application to a model of fermionic atoms in a harmonic trap. The corresponding density profile exhibits a plateau of integer occupation at low temperatures which melts away for higher temperatures., Comment: 14 pages, 11 figures

A time-dependent density functional theory (TDDFT) for a quantum many-body system on a lattice is formulated rigorously. We prove the uniqueness of the density-to-potential mapping and demonstrate that a given density is $v$-representable if the initial many-body state and the density satisfy certain well defined conditions. In particular, we show that for a system evolving from its ground state any density with a continuous second time derivative is $v$-representable and therefore the lattice TDDFT is guaranteed to exist. The TDDFT existence and uniqueness theorem is valid for any connected lattice, independently of its size, geometry and/or spatial dimensionality. The general statements of the existence theorem are illustrated on a pedagogical exactly solvable example which displays all details and subtleties of the proof in a transparent form. In conclusion we briefly discuss remaining open problems and directions for a future research., Comment: 12 pages, 1 figure

In this paper we further explore and develop the quantum continuum mechanics (CM) of [Tao \emph{et al}, PRL{\bf 103},086401] with the aim of making it simpler to use in practice. Our simplifications relate to the non-interacting part of the CM equations, and primarily refer to practical implementations in which the groundstate stress tensor is approximated by its Kohn-Sham version. We use the simplified approach to directly prove the exactness of CM for one-electron systems via an orthonormal formulation. This proof sheds light on certain physical considerations contained in the CM theory and their implication on CM-based approximations. The one-electron proof then motivates an approximation to the CM (exact under certain conditions) expanded on the wavefunctions of the Kohn-Sham (KS) equations. Particular attention is paid to the relationships between transitions from occupied to unoccupied KS orbitals and their approximations under the CM. We also demonstrate the simplified CM semi-analytically on an example system.

We extend a recent formulation of quantum continuum mechanics [J. Tao et. al, Phys. Rev. Lett. {\bf 103}, 086401 (2009)] to many-body systems subjected to a magnetic field. To accomplish this, we propose a modified Lagrangian approach, in which motion of infinitesimal volume elements of the system is referred to the "quantum convective motion" that the magnetic field produces already in the ground-state of the system. In the linear approximation, this approach results in a redefinition of the elastic displacement field $\uv$, such that the particle current $\jv$ contains both an electric displacement and a magnetization contribution: $\jv=\jv_0+n_0\partial_t \uv+\nabla \times (\jv_0\times \uv)$, where $n_0$ and $\jv_0$ are the particle density and the current density of the ground-state and $\partial_t$ is the partial derivative with respect to time. In terms of this displacement, we formulate an "elastic approximation" analogous to the one proposed in the absence of magnetic field. The resulting equation of motion for $\uv$ is expressed in terms of ground-state properties -- the one-particle density matrix and the two-particle pair correlation function -- and in this form it neatly generalizes the equation obtained for vanishing magnetic field., Comment: 13 pages, revised version accepted to PRB

To address the impact of electron correlations in the linear and non-linear response regimes of interacting many-electron systems exposed to time-dependent external fields, we study one-dimensional (1D) systems where the interacting problem is solved exactly by exploiting the mapping of the 1D $N$-electron problem onto an $N$-dimensional single electron problem. We analyze the performance of the recently derived 1D local density approximation as well as the exact-exchange orbital functional for those systems. We show that the interaction with an external resonant laser field shows Rabi oscillations which are detuned due to the lack of memory in adiabatic approximations. To investigate situations where static correlations play a role, we consider the time-evolution of the natural occupation numbers associated to the reduced one-body density matrix. Those studies shed light on the non-locality and time-dependence of the exchange and correlation functionals in time-dependent density and density-matrix functional theories., Comment: 19 pages, 13 figures, version as published apart from layout

Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice this normally means optimizing the value of some observable, a so called merit function. In consequence, a key part of the theory is a set of equations, which provides the gradient of the merit function with respect to parameters that control the shape of the driving field. We show that these equations can be straightforwardly derived using the standard linear response theory, only requiring a minor generalization -- the unperturbed Hamiltonian is allowed to be time-dependent. As a result, the aforementioned gradients are identified with certain response functions. This identification leads to a natural reformulation of QOCT in term of the Keldysh contour formalism of the quantum many-body theory. In particular, the gradients of the merit function can be calculated using the diagrammatic technique for non-equilibrium Green's functions, which should be helpful in the application of QOCT to computationally difficult many-electron problems., Comment: 7 pages

Through the exact solution of a two-electron system interacting with a monochromatic laser we prove that all adiabatic density functionals within time-dependent density-functional theory are not able to discern between resonant and non-resonant (detuned) Rabi oscillations. This is rationalized in terms of a fictitious dynamical exchange-correlation (xc) detuning of the resonance while the laser is acting. The non-linear dynamics of the Kohn-Sham system shows the characteristic features of detuned Rabi oscillations even if the exact resonant frequency is used. We identify the source of this error in a contribution from the xc-functional to the non-linear equations describing the electron dynamics in an effective two-level system. The constraint of preventing the detuning introduces a new strong condition to be satisfied by approximate xc-functionals.

We present a local density approximation (LDA) for one-dimensional (1D) systems interacting via the soft-Coulomb interaction based on quantum Monte-Carlo calculations. Results for the ground-state energies and ionization potentials of finite 1D systems show excellent agreement with exact calculations, obtained by exploiting the mapping of an $N$-electron system in $d$ dimensions, onto a single electron in $N\times d$ dimensions properly symmetrized by the Young diagrams. We conclude that 1D LDA is of the same quality as its three-dimensional (3D) counterpart, and we infer conclusions about 3D LDA. The linear and non-linear time-dependent responses of 1D model systems using LDA, exact exchange, and the exact solution are investigated and show very good agreement in both cases, except for the well known problem of missing double excitations. Consequently, the 3D LDA is expected to be of good quality beyond linear response. In addition, the 1D LDA should prove useful in modeling the interaction of atoms with strong laser fields, where this specific 1D model is often used., Comment: 5 pages, 3 figures

It is shown that the density-potential mapping and the ${\cal V}$-representability problems in the time-dependent current density functional theory (TDCDFT) are reduced to the solution of a certain many-body nonlinear Schr\"odinger equation (NLSE). The derived NLSE for TDCDFT adds a link which bridges the earlier NLSE-based formulations of the time-dependent deformation functional theory (TDDefFT) and the time-dependent density functional theory (TDDFT). We establish close relations between the nonlinear many-body problems which control the existence of TDCDFT, TDDFT, and TDDefFT, and thus develop a unified point of view on the whole family of the TDDFT-like theories., Comment: RevTeX4, 15 pages

A rigorous formulation of time-dependent current density functional theory (TDCDFT) on a lattice is presented. The density-to-potential mapping and the ${\cal V}$-representability problems are reduced to a solution of a certain nonlinear lattice Schr\"odinger equation, to which the standard existence and uniqueness results for nonliner differential equations are applicable. For two versions of the lattice TDCDFT we prove that any continuous in time current density is locally ${\cal V}$-representable (both interacting and noninteracting), provided in the initial state the local kinetic energy is nonzero everywhere. In most cases of physical interest the ${\cal V}$-representability should also hold globally in time. These results put the application of TDCDFT to any lattice model on a firm ground, and open a way for studying exact properties of exchange correlation potentials., Comment: revtex4, 9 pages

We present an analytical study of the D'yakonov-Perel' spin relaxation time for degenerate electrons in a photo-excited electron-hole liquid in intrinsic semiconductors exhibiting a spin-split band structure. The D'yakonov-Perel' spin relaxation of electrons in these materials is controlled by electron-hole scattering, with small corrections from electron-electron scattering and virtually none from electron-impurity scattering. We derive simple expressions (one-dimensional and two-dimensional integrals respectively) for the effective electron-hole and electron-electron scattering rates which enter the spin relaxation time calculation. The electron-hole scattering rate is found to be comparable to the scattering rates from impurities in the electron liquid - a common model for n-type doped semiconductors. As the density of electron-hole pairs decreases (within the degenerate regime), a strong enhancement of the scattering rates and a corresponding slowing down of spin relaxation is predicted due to exchange and correlation effects in the electron-hole liquid. In the opposite limit of high density, the original D'yakonov-Perel' model fails due to decreasing scattering rates and is eventually superseded by free precession of individual quasiparticle spins., Comment: 16 pages, 5 figures

We study spin dynamics in a two-dimensional electron gas with a pure gauge non-Abelian spin-orbit field, for which systems with balanced Rashba and Dresselhaus spin-orbit couplings, and the (110)-axis grown GaAs quantum wells are typical examples. We demonstrate the duality of the spin evolution and the electron-density dynamics in a system without spin-orbit coupling, which considerably simplifies and deepens the analysis of spin-dependent processes. This duality opens a venue for the understanding of this class of systems, highly interesting for their applications in spintronics, through known properties of the systems without spin-orbit coupling., Comment: version accepted to PRB, revtex4, 4+ pages, 1 figure

It is shown that an electric field applied to p-doped graphane generates a dissipationless orbital momentum Hall current. In the clean limit the corresponding Hall conductivity is independent of the concentration of holes. The Hall effect is related to the $2\pi$-Berry phase accumulated when heavy and light holes are transported around the degeneracy point in the center of the Brillouin zone. This also leads to the orbital momentum edge currents in the equilibrium state, and to the accumulation of the orbital momentum at the edges when the system is driven out of equilibrium., Comment: RevTeX 4, 4 pages, 2 figures, final version

We express the high-frequency (anti-adiabatic) limit of the exchange-correlation kernels of an inhomogeneous electron gas in terms of the following equilibrium properties: the ground-state density, the kinetic stress tensor, the pair-correlation function, and the ground-state exchange-correlation potential. Of these quantities, the first three are amenable to exact evaluation by Quantum Monte Carlo methods, while the last can be obtained from the inversion of the Kohn-Sham equation for the ground-state orbitals. The exact scalar kernel, in this limit, is found to be of very long range in space, at variance with the kernel that is used in the standard local density approximation. The anti-adiabatic xc kernels should be useful in calculations of excitation energies by time-dependent DFT in atoms, molecules, and solids, and provides a solid basis for interpolation between the low- and high-frequency limits of the xc kernels., Comment: 9 pages, 3 figures, to be submitted to PRB

We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-particle orbitals. We refer to our approach as continuum mechanics for quantum many-body systems. In the linear response regime, the equation of motion for the displacement field becomes a linear fourth-order integro-differential equation, whose only inputs are the one-particle density matrix and the pair correlation function of the ground-state. The complexity of this equation remains essentially unchanged as the number of particles increases. We show that our equation of motion is a hermitian eigenvalue problem, which admits a complete set of orthonormal eigenfunctions under a scalar product that involves the ground-state density. Further, we show that the excitation energies derived from this approach satisfy a sum rule which guarantees the exactness of the integrated spectral strength. Our formulation becomes exact for systems consisting of a single particle, and for any many-body system in the high-frequency limit. The theory is illustrated by explicit calculations for simple one- and two-particle systems., Comment: 23 pages, 4 figures, 1 table, 6 Appendices This paper is a follow-up to PRL 103, 086401 (2009)

We investigate the suitability of natural orbitals as a basis for describing many-body excitations. We analyze to which extend the natural orbitals describe both bound as well as ionized excited states and show that depending on the specifics of the excited state the ground-state natural orbitals yield a good approximation or not. We show that the success of reduced density-matrix functional theory in describing molecular dissociation lies in the flexibility provided by fractional occupation numbers while the role of the natural orbitals is minor., Comment: 9 pages, 6 figures

We develop a gauge theory for diffusive and precessional spin dynamics in two-dimensional electron gas with disorder. Our approach reveals a direct connections between the absence of the equilibrium spin current and strong anisotropy in the spin relaxation: both effects arise if the spin-orbit coupling is reduced to a pure gauge SU(2) field. In this case, by a gauge transformation in the form of a local SU(2) rotation in the spin subspace the spin-orbit coupling can be removed. The resulting spin dynamics is exactly described in terms of two kinetic coefficients: the spin diffusion and electron mobility. After the inverse transformation, full diffusive and precessional spin density dynamics, including the anisotropic spin relaxation, formation of stable spin structures, and spin precession induced by a macroscopic current, is restored. Explicit solutions of the spin evolution equations are found for the initially uniform spin density and for stable nonuniform structures. Our analysis demonstrates a universal relation between the spin relaxation rate and spin diffusion coefficient., Comment: published version, minor corrections

The dissociation of molecules, even the most simple hydrogen molecule, cannot be described accurately within density functional theory because none of the currently available functionals accounts for strong on-site correlation. This problem has led to a discussion of properties that the local Kohn-Sham potential has to satisfy in order to correctly describe strongly correlated systems. We derive an analytic expression for this potential at the dissociation limit and show that the numerical calculations for a one-dimensional two electron model system indeed approach and reach this limit. It is shown that the functional form of the potential is universal, i.e. independent of the details of the system., Comment: 17 pages, 3 figures, submitted to JCP

We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the time-dependent wave function in a locally co-moving reference frame can be described as a geometric deformation of the ground-state wave function. We show that this equation of motion is exact for systems consisting of a single particle, and for all systems at sufficiently high frequency, and that it leads to an excitation spectrum that has the correct integrated strength. The theory is illustrated by simple model applications to one- and two-electron systems., Comment: 4 pages, 1 figure, 1 table

The logical structure and the basic theorems of time-dependent current density functional theory (TDCDFT) are analyzed and reconsidered from the point of view of recently proposed time-dependent deformation functional theory (TDDefFT). It is shown that the formalism of TDDefFT allows to avoid a traditional external potential-to-density/current mapping. Instead the theory is formulated in a form similar to the constrained search procedure in the ground state DFT. Within this formulation of TDCDFT all basic functionals appear from the solution of a constrained universal many-body problem in a comoving reference frame, which is equivalent to finding a conditional extremum of a certain universal action functional. As a result the physical origin of the universal functionals entering the theory, as well as their proper causal structure becomes obvious. In particular, this leaves no room for any doubt concerning predictive power of the theory., Comment: revtex4, 24 pages

Spin-currents and non-abelian gauge potentials in electronic systems can be treated by spin-current-density functional theory, whose main input is the exchange-correlation (xc) energy expressed as a functional of spin-currents. Constructing a functional of spin currents that is invariant under U(1)$\times$SU(2) transformations is a long-standing challenge. We solve the problem by expressing the energy as a functional of a new variable we call "invariant vorticity". As an illustration we construct the xc energy functional for a two-dimensional electron gas with linear spin-orbit coupling and show that it is proportional to the fourth power of the spin current., Comment: 8 pages, 3 figures, submitted

We show that the Lorentz shear modulus of macroscopically homogeneous electronic states in the lowest Landau level is proportional to the bulk modulus of an equivalent system of interacting classical particles in the thermodynamic limit. Making use of this correspondence we calculate the Lorentz shear modulus of Laughlin's fractional quantum Hall states at filling factor $\nu=1/m$ ($m$ an odd integer) and find that it is equal to $\pm \hbar mn/4$, where $n$ is the density of particles and the sign depends on the direction of magnetic field. This is in agreement with the recent result obtained by Read in arXiv:0805.2507 and corrects our previous result published in Phys. Rev. B {\bf 76}, 161305 (R) (2007)., Comment: 8 pages, 3 figures