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The Fermilab Proton-Improvement-Plan-II (PIP-II) is being implemented in order to support the precision neutrino oscillation measurements at the Deep Underground Neutrino Experiment, the U.S. flagship neutrino experiment. The PIP-II LINAC is presently under construction and is expected to provide 800~MeV protons with 2~mA current. This white paper summarizes the outcome of the first workshop on May 10 through 13, 2023, to exploit this capability for new physics opportunities in the kinematic regime that are unavailable to other facilities, in particular a potential beam dump facility implemented at the end of the LINAC. Various new physics opportunities have been discussed in a wide range of kinematic regime, from eV scale to keV and MeV. We also emphasize that the timely establishment of the beam dump facility at Fermilab is essential to exploit these new physics opportunities.

The Snowmass report on rare processes and precision measurements recommended Mu2e-II and a next generation muon facility at Fermilab (Advanced Muon Facility) as priorities for the frontier. The Workshop on a future muon program at FNAL was held in March 2023 to discuss design studies for Mu2e-II, organizing efforts for the next generation muon facility, and identify synergies with other efforts (e.g., muon collider). Topics included high-power targetry, status of R&D for Mu2e-II, development of compressor rings, FFA and concepts for muon experiments (conversion, decays, muonium and other opportunities) at AMF. This document summarizes the workshop discussions with a focus on future R&D tasks needed to realize these concepts., Comment: 68 pages, 36 figures

Intelligence analysts face a difficult problem: distinguishing extremist rhetoric from potential extremist violence. Many are content to express abuse against some target group, but only a few indicate a willingness to engage in violence. We address this problem by building a predictive model for intent, bootstrapping from a seed set of intent words, and language templates expressing intent. We design both an n-gram and attention-based deep learner for intent and use them as colearners to improve both the basis for prediction and the predictions themselves. They converge to stable predictions in a few rounds. We merge predictions of intent with predictions of abusive language to detect posts that indicate a desire for violent action. We validate the predictions by comparing them to crowd-sourced labelling. The methodology can be applied to other linguistic properties for which a plausible starting point can be defined.

At low temperatures, indirect excitons formed at the in-plane electron-hole interface in a coupled quantum well structure undergo a spontaneous transition into a spatially modulated state. We report on the control of the instability wavelength, measurement of the dynamics of the exciton emission pattern, and observation of the fluctuation and commensurability effect of the exciton density wave. We found that fluctuations are strongly suppressed when the instability wavelength is commensurate with defect separation along the exciton density wave. The commensurability effect is also found in numerical simulations within the model describing the exciton density wave in terms of an instability due to stimulated processes.

Following the experimental realization of Dicke superradiance in Bose gases coupled to cavity light fields, we investigate the behavior of ultra cold fermions in a transversely pumped cavity. We focus on the equilibrium phase diagram of spinless fermions coupled to a single cavity mode and establish a zero temperature transition to a superradiant state. In contrast to the bosonic case, Pauli blocking leads to lattice commensuration effects that influence self-organization in the cavity light field. This includes a sequence of discontinuous transitions with increasing atomic density and tricritical superradiance. We discuss the implications for experiment.

We explore the far from equilibrium response of a holographic superfluid using the AdS/CFT correspondence. We establish the dynamical phase diagram corresponding to quantum quenches of the order parameter source field. We find three distinct regimes of behaviour that are related to the spectrum of black hole quasi-normal modes. These correspond to damped oscillations of the order parameter, and over-damped approaches to the superfluid and normal states. The presence of three regimes, which includes an emergent dynamical temperature scale, is argued to occur more generally in time-reversal invariant systems that display continuous symmetry breaking., Comment: 6 pages, 4 figures; v2 minor changes, version published in PRL

We explore the zero-temperature phase diagram of bosons interacting via Feshbach resonant pairing interactions in one dimension. Using DMRG (Density Matrix Renormalization Group) and field theory techniques we characterize the phases and quantum phase transitions in this low-dimensional setting. We provide a broad range of evidence in support of an Ising quantum phase transition separating distinct paired superfluids, including results for the energy gaps, correlation functions and entanglement entropy. In particular, we show that the Ising correlation length, order parameter and critical properties are directly accessible from a ratio of the atomic and molecular two-point functions. We further demonstrate that both the zero-momentum occupation numbers and the visibility are in accordance with the absence of a purely atomic superfluid phase. We comment on the connection to recent studies of boson pairing in a generalized classical XY model., Comment: 18 pages, 22 figures

Motivated by experiments observing self-organization of cold atoms in optical cavities we investigate the collective dynamics of the associated nonequilibrium Dicke model. The model displays a rich semiclassical phase diagram of long time attractors including distinct superradiant fixed points, bistable and multistable coexistence phases and regimes of persistent oscillations. We explore the intrinsic timescales for reaching these asymptotic states and discuss the implications for finite duration experiments. On the basis of a semiclassical analysis of the effective Dicke model we find that sweep measurements over 200ms may be required in order to access the asymptotic regime. We briefly comment on the corrections that may arise due to quantum fluctuations and states outside of the effective two-level Dicke model description., Comment: 27 pages, 20 figures

We explore the Mott insulating state of single-band bosonic pairing Hamiltonians using analytical approaches and large scale density matrix renormalization group calculations. We focus on the second Mott lobe which exhibits a magnetic quantum phase transition in the Ising universality class. We use this feature to discuss the behavior of a range of physical observables within the framework of the 1D quantum Ising model and the strongly anisotropic Heisenberg model. This includes the properties of local expectation values and correlation functions both at and away from criticality. Depending on the microscopic interactions it is possible to achieve either antiferromagnetic or ferromagnetic exchange interactions and we highlight the possibility of observing the E8 mass spectrum for the critical Ising model in a longitudinal magnetic field., Comment: 14 pages, 15 figures

We investigate the phase diagram of bosons interacting via Feshbach-resonant pairing interactions in a one-dimensional lattice. Using large scale density matrix renormalization group (DMRG) and field theory techniques we explore the atomic and molecular correlations in this low-dimensional setting. We provide compelling evidence for an Ising deconfinement transition occurring between distinct superfluids and extract the Ising order parameter and correlation length of this unusual superfluid transition. This is supported by results for the entanglement entropy which reveal both the location of the transition and critical Ising degrees of freedom on the phase boundary., Comment: 4 pages, 4 figures

We explore the phase diagram of two-component bosons with Feshbach resonant pairing interactions in an optical lattice. It has been shown in previous work to exhibit a rich variety of phases and phase transitions, including a paradigmatic Ising quantum phase transition within the second Mott lobe. We discuss the evolution of the phase diagram with system parameters and relate this to the predictions of Landau theory. We extend our exact diagonalization studies of the one-dimensional bosonic Hamiltonian and confirm additional Ising critical exponents for the longitudinal and transverse magnetic susceptibilities within the second Mott lobe. The numerical results for the ground state energy and transverse magnetization are in good agreement with exact solutions of the Ising model in the thermodynamic limit. We also provide details of the low-energy spectrum, as well as density fluctuations and superfluid fractions in the grand canonical ensemble., Comment: 11 pages, 14 figures. To appear in Phys. Rev. A

Recent experiments on Bose--Einstein condensates in optical cavities have reported a quantum phase transition to a coherent state of the matter-light system -- superradiance. The time dependent nature of these experiments demands consideration of collective dynamics. Here we establish a rich phase diagram, accessible by quench experiments, with distinct regimes of dynamics separated by non-equilibrium phase transitions. We include the key effects of cavity leakage and the back-reaction of the cavity field on the condensate. Proximity to some of these phase boundaries results in critical slowing down of the decay of many-body oscillations. Notably, this slow decay can be assisted by large cavity losses. Predictions include the frequency of collective oscillations, a variety of multi-phase co-existence regions, and persistent optomechanical oscillations described by a damped driven pendulum. These findings open new directions to study collective dynamics and non-equilibrium phase transitions in matter-light systems., Comment: 5 pages, 5 figures

The phase diagram of Sr3Ru2O7 contains a metamagnetic transition that bifurcates to enclose an anomalous phase with intriguing properties - a large resistivity with anisotropy that breaks the crystal-lattice symmetry. We propose that this is a magnetic analogue of the spatially inhomogeneous superconducting Fulde-Ferrell-Larkin-Ovchinnikov state. Based on a microscopic theory of Stoner magnetism we derive a Ginzburg-Landau expansion where the magnetisation transverse to the applied field can become spatially inhomogeneous. We show that this reproduces the observed phase diagram of Sr3Ru2O7., Comment: 20 pages, 16 figures; revisions to text and figures

We present a microscopic model of the quantum paraelectric-ferroelectric phase transition with a focus on the influence of coupled fluctuating phonon modes. These may drive the continuous phase transition first order through a metaelectric transition and furthermore stimulate the emergence of a textured phase that preempts the transition. We discuss two further consequences of fluctuations, firstly for the heat capacity, and secondly we show that the inverse paraelectric susceptibility displays T^2 quantum critical behavior, and can also adopt a characteristic minimum with temperature. Finally, we discuss the observable consequences of our results., Comment: 5 pages, 2 figures

We report on the measurements of the kinetics of expanding and collapsing rings in the exciton emission pattern. The rings are found to preserve their integrity during expansion and collapse, indicating that the observed kinetics is controlled by charge carrier transport rather than by a much faster process of exciton production and decay. The relation between ring kinetics and carrier transport, revealed by our experiment and confirmed by comparison with a theoretical model, is used to determine electron and hole transport characteristics in a contactless fashion., Comment: 6 pages, 4 figures

Recent experiments on strongly coupled cavity quantum electrodynamics present new directions in "matter-light" systems. Following on from our previous work [Phys. Rev. Lett. 102, 135301 (2009)] we investigate Bose-Hubbard models coupled to a cavity light field. We discuss the emergence of photoexcitations or "polaritons" within the Mott phase, and obtain the complete variational phase diagram. Exploiting connections to the super-radiance transition in the Dicke model we discuss the nature of polariton condensation within this novel state. Incorporating the effects of carrier superfluidity, we identify a first-order transition between the superradiant Mott phase and the single component atomic superfluid. The overall predictions of mean field theory are in excellent agreement with exact diagonalization and we provide details of superfluid fractions, density fluctuations, and finite size effects. We highlight connections to recent work on coupled cavity arrays., Comment: 16 pages, 17 figures

Alongside superfluidity, itinerant (Stoner) ferromagnetism remains one of the most well-characterized phases of correlated Fermi systems. A recent experiment has reported the first evidence for novel phase behavior on the repulsive side of the Feshbach resonance in a two-component ultracold Fermi gas. By adapting recent theoretical studies to the atomic trap geometry, we show that an adiabatic ferromagnetic transition would take place at a weaker interaction strength than is observed in experiment. This discrepancy motivates a simple non-equilibrium theory that takes account of the dynamics of magnetic defects and three-body losses. The formalism developed displays good quantitative agreement with experiment., Comment: 4 pages, 2 figures

A variety of analytical techniques suggest that quantum fluctuations lead to a fundamental instability of the Fermi liquid that drives ferromagnetic transitions first order at low temperatures. We present both analytical and numerical evidence that, driven by the same quantum fluctuations, this first order transition is pre-empted by the formation of an inhomogeneous magnetic phase. This occurs in a manner that is closely analogous to the formation of the inhomogeneous superconducting Fulde-Ferrel-Larkin-Ovchinnikov state. We derive these results from a field theoretical approach supplemented with numerical Quantum Monte Carlo simulations. Our analytical approach represents a considerable simplification over diagrammatic methods, makes contact with older analyses of the unitarity limit, and enables a simple physical picture to emerge., Comment: 5 pages, 2 figures

Motivated by experiments on heteronuclear Feshbach resonances in Bose mixtures, we investigate s-wave pairing of two species of bosons in an optical lattice. The zero temperature phase diagram supports a rich array of superfluid and Mott phases and a network of quantum critical points. This topology reveals an underlying structure that is succinctly captured by a two-component Landau theory. Within the second Mott lobe we establish a quantum phase transition described by the paradigmatic longitudinal and transverse field Ising model. This is confirmed by exact diagonalization of the 1D bosonic Hamiltonian. We also find this transition in the homonuclear case., Comment: 5 pages, 4 figures

We investigate ferromagnetic ordering in an itinerant ultracold atomic Fermi gas with repulsive interactions and population imbalance. In a spatially uniform system, we show that at zero temperature the transition to the itinerant magnetic phase transforms from first to second order with increasing population imbalance. Drawing on these results, we elucidate the phases present in a trapped geometry, finding three characteristic types of behavior with changing population imbalance. Finally, we outline the potential experimental implications of the findings., Comment: 10 pages, 4 figures, typos added, references added

Motivated by recent experiments on cold atomic gases in ultra high finesse optical cavities, we consider the problem of a two-band Bose--Hubbard model coupled to quantum light. Photoexcitation promotes carriers between the bands and we study the non-trivial interplay between Mott insulating behavior and superfluidity. The model displays a global U(1) X U(1) symmetry which supports the coexistence of Mott insulating and superfluid phases, and yields a rich phase diagram with multicritical points. This symmetry property is shared by several other problems of current experimental interest, including two-component Bose gases in optical lattices, and the bosonic BEC-BCS crossover problem for atom-molecule mixtures induced by a Feshbach resonance. We corroborate our findings by numerical simulations., Comment: 4 pages, 3 figures

The phase diagram of Sr3Ru2O7 contains a metamagnetic transition that bifurcates to enclose an anomalous phase with intriguing properties - a large resistivity with anisotropy that breaks the crystal-lattice symmetry. We propose that this is a magnetic analogue of the spatially inhomogeneous superconducting Fulde-Ferrel-Larkin-Ovchinnikov state. We show - through a Ginzburg-Landau expansion where the magnetisation transverse to the applied field can become spatially inhomogeneous - that a Stoner model with electronic band dispersion can reproduce this phase diagram and transport behaviour., Comment: 5 pages, 4 figures; revisions to text

We explore the zero temperature phase behavior of a two-dimensional two-component atomic Fermi gas with population and mass imbalance in the regime of the BEC-BCS crossover. Working in the mean-field approximation, we show that the normal and homogeneous balanced superfluid phases are separated by an inhomogeneous superfluid phase of Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) type. We obtain an analytical expression for the line of continuous transitions separating the normal and inhomogeneous FFLO phases. We further show that the transition from the FFLO phase to the homogeneous balanced superfluid is discontinuous leading to phase separation. If the species have different masses, the superfluid phase is favored when the lighter species is in excess. We explore the implications of these findings for the properties of the two-component Fermi gas in the atomic trap geometry. Finally, we compare and contrast our findings with the predicted phase behavior of the electron-hole bilayer system., Comment: 11 pages, 6 figures. Accepted by Phys. Rev. A

We have studied the competition and coexistence of staggered triplet SC with d-wave singlet SC and SDW in the mean-field approximation. Detailed numerical studies demonstrate that particle-hole asymmetry mixes these states and therefore they are simultaneously present. Even more interesting were the results of our study of the influence of a uniform magnetic field. We observe novel transitions that show the characteristics of Fulde-Ferrel phases, yet they concern transitions to different combinations of the above orders. For example, above a given field, in a particle-hole symmetric system we observe a transition from d-wave singlet SC to a state in which d-wave singlet SC coexists with staggered triplet SC and SDW. We believe our results may provide, among others, a direct explanation to recent puzzles about the Fulde Ferrel like states that are apparently observed in CeCoIn5., Comment: To be published in J. Phys. Cond. Mat

We show that the recently proposed ionic microscope set-up [Kollath et.al, PRA, \textbf{76}, 063602 (2007)] could be adapted to measure the \textit {local single-particle energy distribution} of a degenerate Fermi gas \textit{in situ} with the resolution on the nanometer scale. We study an ion held in a Paul trap in an atomic Fermi gas and compute the two-photon Raman photo-association rate of the ion and an atom. We show that, as a function of the detunings between the frequencies of the two incident lasers and energies in the atom-ion system, the photo-association rate directly measures the single-particle energy distribution in the Fermi gas around the ion. We describe an experiment to measure the photo-association rate of a trapped ion and argue that, as the position of the ion can be scanned through the Fermi gas, this experiment directly probes the local energy and spin-state distribution of the Fermi gas., Comment: 5 pages, 2 figures

Motivated by recent experimental work, we use first-principles density functional theory methods to conduct an extensive search for low enthalpy structures of C$_6$Ca under pressure. As well as a range of buckled structures, which are energetically competitive over an intermediate range of pressures, we show that the high pressure system ($\gtrsim 18$ GPa) is unstable towards the formation of a novel class of layered structures, with the most stable compound involving carbon sheets containing five- and eight-membered rings. As well as discussing the energetics of the different classes of low enthalpy structures, we comment on the electronic structure of the high pressure compound and its implications for superconductivity., Comment: 4 pages 4 figures

We consider a two-component atomic Fermi gas within a mean-field, single-channel model, where both the mass and population of each component are unequal. We show that the tricritical point at zero temperature evolves smoothly from the BEC- to BCS-side of the resonance as a function of mass ratio r. We find that the interior gap state proposed by Liu and Wilczek is always unstable to phase separation, while the breached pair state with one Fermi surface for the excess fermions exhibits differences in its DoSs and pair correlation functions depending on which side of the resonance it lies. Finally, we show that, when r > 3.95, the finite temperature phase diagram of trapped gases at unitarity becomes topologically distinct from the equal mass system., Comment: 5 pages, 5 figures

The two-component Fermi gas is the simplest fermion system displaying superfluidity, and as such finds applications ranging from the theory of superconductivity to QCD. Ultracold atomic gases provide an exceptionally clean realization of this system, where the interatomic interaction and the atom species population are both independent, tuneable parameters. This allows one to investigate the Fermi gas with imbalanced spin populations, which had previously been experimentally elusive, and this prospect has stimulated much theoretical activity. Here we show that the finite temperature phase diagram contains a region of phase separation between the superfluid and normal states that touches the boundary of second-order superfluid transitions at a tricritical point, reminiscent of the phase diagram of $^3$He-$^4$He mixtures. A variation of interaction strength then results in a line of tricritical points that terminates at zero temperature on the molecular Bose-Einstein condensate (BEC) side. On this basis, we argue that tricritical points will play an important role in the recent experiments on polarised atomic Fermi gases., Comment: 6 pages, 4 figures. Manuscript extended and figures modified. For final version, see Nature Physics

We discuss models of the modulational instability in a cold exciton system in coupled quantum wells. One mechanism involves exciton formation in a photoexcited electron-hole system in the presence of stimulated binding processes which build up near exciton degeneracy. It is shown that such processes may give rise to Turing instability leading to a spatially modulated state. The structure and symmetry of resulting patterns depend on dimensionality and symmetry. In the spatially uniform 2d electron-hole system, the instability leads to a triangular lattice pattern while, at an electron-hole interface, a periodic 1d pattern develops. Wavelength selection mechanism is analyzed, revealing that the transition is abrupt (type I) for the uniform 2d system, and continuous (type II) for the electron-hole interface. Another mechanism that could possibly drive the instability involves long-range attraction of the excitons. We illustrate how such an interaction can result from current induced by exciton recombination ('plasmon wind'), derive stability criterion, and discuss likelihood of such a scenario., Comment: 6 pages, 2 figures, proceedings of International Conference on Spontaneous Coherence in Exciton Systems

Although not an intrinsic superconductor, it has been long--known that, when intercalated with certain dopants, graphite is capable of exhibiting superconductivity. Of the family of graphite--based materials which are known to superconduct, perhaps the most well--studied are the alkali metal--graphite intercalation compounds (GIC) and, of these, the most easily fabricated is the C${}_8$K system which exhibits a transition temperature $\bm{T_c\simeq 0.14} $K. By increasing the alkali metal concentration (through high pressure fabrication techniques), the transition temperature has been shown to increase to as much as $\bm 5 $K in C${}_2$Na. Lately, in an important recent development, Weller \emph{et al.} have shown that, at ambient conditions, the intercalated compounds \cyb and \cca exhibit superconductivity with transition temperatures $\bm{T_c\simeq 6.5} $K and $\bm{11.5} $K respectively, in excess of that presently reported for other graphite--based compounds. We explore the architecture of the states near the Fermi level and identify characteristics of the electronic band structure generic to GICs. As expected, we find that charge transfer from the intercalant atoms to the graphene sheets results in the occupation of the $\bm\pi$--bands. Yet, remarkably, in all those -- and only those -- compounds that superconduct, we find that an interlayer state, which is well separated from the carbon sheets, also becomes occupied. We show that the energy of the interlayer band is controlled by a combination of its occupancy and the separation between the carbon layers., Comment: 4 Figures. Please see accompanying experimental manuscript "Superconductivity in the Intercalated Graphite Compounds C6Yb and C6Ca" by Weller et al

Condensation of microcavity polaritons and the substantial influence of pair-breaking disorder and decoherence leading to a laser regime has been recently considered using two different models: a model for direct two band excitons in a disordered quantum well coupled to light and a model where the cavity mode couples instead to a medium of localised excitons, represented by two-level oscillators in the presence of dephasing processes. Even if complementary from the point of view of assumptions, the models share most of the main conclusions and show similar phase diagrams. The issue whether excitons are propagating or localised seems secondary for the polariton condensation and the way in which pair-breaking disorder and decoherence processes influence the condensation and drive the microcavity into a lasing regime is, within the approximations used in each model, generic. The reasons for the similarities between the two physical situations are analysed and explained., Comment: Proceeding of the First International Conference on Spontaneous Coherence in Excitonic Systems (ICSCE'04); 7 pages, 2 eps figures

We study the short-time dynamics of a degenerate Fermi gas positioned near a Feshbach resonance following an abrupt jump in the atomic interaction resulting from a change of external magnetic field. We investigate the dynamics of the condensate order parameter and pair wavefunction for a range of field strengths. When the abrupt jump is sufficient to span the BCS to BEC crossover, we show that the rigidity of the momentum distribution precludes any atom-molecule oscillations in the entrance channel dominated resonances observed in the 40K and 6Li. Focusing on material parameters tailored to the 40K Feshbach resonance system at 202.1 gauss, we comment on the integrity of the fast sweet projection technique as a vehicle to explore the condensed phase in the crossover region, Comment: 5 pages, 4 figures

The bilayer ruthenate Sr_3Ru_2O_7 has been cited as a textbook example of itinerant metamagnetic quantum criticality. However, recent studies of the ultra-pure system have revealed striking anomalies in magnetism and transport in the vicinity of the quantum critical point. Drawing on new experimental data, we propose that the anomalous phase behavior can be accommodated by a mechanism which relies on the effects of strong magnetoelastic coupling. We argue that the phenomenological theory identified here is more generic and raises the possibility of quantum tricritical behaviour., Comment: 5pages, 4 figures. Text revised for clarity and some more experimental data included

Studies of Feshbach resonance phenomena in fermionic alkali gases have drawn heavily on the intuition afforded by a Fermi-Bose theory which presents the Feshbach molecule as a featureless Bose particle. While this model may provide a suitable platform to explore the lithium-6 system, we argue that its application to potassium-40, where the hyperfine structure is inverted, is inappropriate. Introducing a three-state Fermi model, where a spin state is shared by the open and closed channel states, we show that effects of ``Pauli blocking'' are recorded in the internal structure of the condensate wave function., Comment: References added, Fig.1 revised, and Fig.3 removed

We study effects of nonmagnetic impurities on the competition between the superconducting and electron-hole pairing. We show that disorder can result in coexistence of these two types of ordering in a uniform state, even when in clean materials they are mutually exclusive., Comment: 11 pages, 6 eps figures; added affiliation; published version

That excitons in solids might condense into a phase-coherent ground state was proposed about 40 years ago, and has been attracting experimental and theoretical attention ever since. Although experimental confirmation has been hard to come by, the concepts released by this phenomenon have been widely influential. This tutorial review discusses general aspects of the theory of exciton and polariton condensates, focussing on the reasons for coherence in the ground state wavefunction, the BCS to Bose crossover(s) for excitons and for polaritons, and the relationship of the coherent condensates to standard lasers., Comment: 27 pages, 6 figures. Submitted for a special issue of J. Phys. Cond. Matt. associated with the EU network "Photon-mediated phenomena in semiconductor nanostructures"

When subject to a pair-breaking perturbation, the pairing susceptibility of a disordered superconductor exhibits substantial long-ranged mesoscopic fluctuations. Focusing on a thin film subject to a parallel magnetic field, it is proposed that the quantum phase transition to the bulk superconducting condensate may be preempted by the formation of a glass-like phase with multi-fractal correlations of a complex order parameter. Although not universal, we argue that such behavior may be a common feature of quantum critical phenomena in disordered environments., Comment: 7 pages, 1 eps figure

A model for direct two band excitons in a disordered quantum well coupled to light in a cavity is investigated. In the limit in which the exciton density is high, we assess the impact of weak `pair-breaking' disorder on the feasibility of condensation of cavity polaritons. The mean-field phase diagram shows a `lower density' region, where the condensate is dominated by electronic excitations and where disorder tends to close the condensate and quench coherence. Increasing the density of excitations in the system, partially due to the screening of Coulomb interaction, the excitations contributing to the condensate become mainly photon-like and coherence is reestablished for any value of disorder. In contrast, in the photon dominated region of the phase diagram, the energy gap of the quasi-particle spectrum still closes when the disorder strength is increased. Above mean-field, thermal, quantum and fluctuations induced by disorder are considered and the spectrum of the collective excitations is evaluated. In particular, it is shown that the angle resolved photon intensity exhibits an abrupt change in its behaviour, going from the condensed to the non-condensed region., Comment: 17 pages, 9 eps figures; published version

The development of a Turing instability to a spatially modulated state in a photoexcited electron-hole system is proposed as a novel signature of exciton Bose statistics. We show that such an instability, which is driven by kinetics of exciton formation, can result from stimulated processes that build up near quantum degeneracy. In the spatially uniform 2d electron-hole system, the instability leads to a triangular lattice pattern while, at an electron-hole interface, a periodic 1d pattern develops. We analyze the mechanism of wavelength selection, and show that the transition is abrupt (type I) for the uniform 2d system, and continuous (type II) for the electron-hole interface., Comment: 5 pages, 3 figures

We use a novel method based on the semi-classical analysis of sigma-models to describe the phenomenon of strong localization in quasi one-dimensional conductors, obtaining the full distribution of transmission eigenvalues. For several symmetry classes, describing random superconducting and chiral Hamiltonians, the target space of the appropriate sigma-model is a (super)group manifold. In these cases our approach turns out to be exact. The results offer a novel perspective on localization., Comment: Published version

The macroscopic exciton rings observed in the photoluminescence (PL) patterns of excitons in coupled quantum wells (CQWs) are explained by a series of experiments and a theory based on the idea of carrier imbalance, transport and recombination. The rings are found to be a source of cold excitons with temperature close to that of the lattice. We explored states of excitons in the ring over a range of temperatures down to 380 mK. These studies reveal a sharp, albeit continuous, second order phase transition to a low-temperature ordered exciton state, characterized by ring fragmentation into a periodic array of aggregates. An instability at the onset of degeneracy in the cold exciton system, due to stimulated exciton formation, is proposed as the transition mechanism., Comment: 8 pages including 4 figures

We explore the influence of an arbitrary external potential perturbation V on the spectral properties of a weakly disordered conductor. In the framework of a statistical field theory of a nonlinear sigma-model type we find, depending on the range and the profile of the external perturbation, two qualitatively different universal regimes of parametric spectral statistics (i.e. cross-correlations between the spectra of Hamiltonians H and H+V). We identify the translational invariance of the correlations in the space of Hamiltonians as the key indicator of universality, and find the connection between the coordinate system in this space which makes the translational invariance manifest, and the physically measurable properties of the system. In particular, in the case of localized perturbations, the latter turn out to be the eigenphases of the scattering matrix for scattering off the perturbing potential V. They also have a purely statistical interpretation in terms of the moments of the level velocity distribution. Finally, on the basis of this analysis, a set of results obtained recently by the authors using random matrix theory methods is shown to be applicable to a much wider class of disordered and chaotic structures., Comment: 16 pages, 7 eps figures (minor changes and reference [17] added)

We establish a general framework to explore parametric statistics of individual energy levels in unitary random matrix ensembles. For a generic confinement potential $W(H)$, we (i) find the joint distribution functions of the eigenvalues of $H$ and $H'=H+V$ for an arbitrary fixed $V$ both for finite matrix size $N$ and in the ``thermodynamic'' $N\to\infty$ limit; (ii) derive many-point parametric correlation functions of the two sets of eigenvalues and show that they are naturally parametrised by the eigenvalues of the reactance matrix for scattering off the ``potential'' $V$; (iii) prove the universality of the correlation functions in unitary ensembles with non-Gaussian non-invariant confinement potential $W(H-V)$; (iv) establish a general scheme for exact calculation of level-number-dependent parametric correlation functions and apply the scheme to the calculation of intra-level velocity autocorrelation function and the distribution of parametric level shifts.

We explore the behaviour of a system which consists of a photon mode dipole coupled to a medium of two-level oscillators in a microcavity in the presence of decoherence. We consider two types of decoherence processes which are analogous to magnetic and non-magnetic impurities in superconductors. We study different phases of this system as the decoherence strength and the excitation density is changed. For a low decoherence we obtain a polariton condensate with comparable excitonic and photonic parts at low densities and a BCS-like state with bigger photon component due to the fermionic phase space filling effect at high densities. In both cases there is a large gap in the density of states. As the decoherence is increased the gap is broadened and suppressed, resulting in a gapless condensate and finally a suppression of the coherence in a low density regime and a laser at high density limit. A crossover between these regimes is studied in a self-consistent way analogous to the Abrikosov and Gor'kov theory of gapless superconductivity., Comment: 17 pages, 8 figures, submitted to PRA

We establish a general framework to explore parametric statistics of individual energy levels in disordered and chaotic quantum systems of unitary symmetry. The method is applied to the calculation of the universal intra-level parametric velocity correlation function and the distribution of level shifts under the influence of an arbitrary external perturbation., Comment: 5 pages; published version with typos corrected

We explore the influence of external perturbations on the energy levels of a Hamiltonian drawn at random from the Gaussian unitary distribution of Hermitian matrices. By deriving the joint distribution function of eigenvalues, we obtain the (n,m)-point parametric correlation function of the initial and final density of states for perturbations of arbitrary rank and strength. A further generalization of these results allows for the incorporation of short-range spatial correlations in diffusive as well as ballistic chaotic structures., Comment: 4 pages, 1 figure

When subject to a weak magnetic impurity distribution, the order parameter and quasi-particle energy gap of a weakly disordered bulk s-wave superconductor are suppressed. In the Born scattering limit, recent investigations have shown that `optimal fluctuations' of the random impurity potential can lead to the nucleation of `domains' of localised states within the gap region predicted by the conventional Abrikosov-Gor'kov mean-field theory, rendering the superconducting system gapless at any finite impurity concentration. By implementing a field theoretic scheme tailored to the weakly disordered system, the aim of the present paper is to extend this analysis to the consideration of magnetic impurities in the unitarity scattering limit. This investigation reveals that the qualitative behaviour is maintained while the density of states exhibits a rich structure., Comment: 18 pages AMSLaTeX (with LaTeX2e), 6 eps figures