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Statistical mechanics characterizes systems in or near equilibrium using in terms of a handful of "state" variables, e.g. temperature, rather than infinitely many degrees of freedom. Statistical physics describes the expansion of the early universe, aspects of black holes, and most fruitfully, phases of matter and their properties. Quantum considerations have improved this understanding over time and revealed new phenomena, especially in complicated "strongly correlated" systems. Topological phases of matter, e.g., are of both fundamental and practical interest: these phases cannot be distinguished locally, unlike ice and water, which also allows them to store and process quantum information in a "fault-tolerant" manner, recently proposed for application to quantum computation. However, above zero temperature, thermal effects can overwrite this information.Recent experiments on isolated systems have raised fundamental questions and revealed new routes to quantum computing. We now know that entanglement, generated dynamically as a quantum state evolves, "hides" local information about the past, producing familiar equilibrium states, described by a temperature. However, many systems do not thermalize: strong disorder can lead to MBL, which supports numerous phenomena forbidden in equilibrium and can protect quantum information at infinite temperature. In particular, both MBL and thermal systems are robust phases of matter, with a novel, athermal phase transition between them. This thesis begins with an overview of MBL and thermalization, followed by an overview of exactly soluble quantum systems. We then turn to an important result in the field by this author: we introduce the first nontrivial example of an integrable Floquet model and comment on its solution and salient features. We then discuss how integrable models can provide insight into quantum thermalization, e.g. in terms of entanglement growth and demonstrating that conserved charges diffuse. We then investigate thermalization away from the integrable limit, also known as "quantum chaos." We review the standard techniques in this field and, briefly, several important results, before reproducing work by this author establishing definitively the long-conjectured result that the onset of thermalization in the presence of a conserved charge is governed by diffusion of said charge. We then investigate the interplay of conventional and topological order with nonequilibrium phase structure, with applications to quantum computation in mind. We review localization-protected quantum order in several models. We then investigate two models with non-Abelian symmetry, and show that MBL in such models can only realize if the symmetry breaks spontaneously to an Abelian subgroup. Finally, we conclude by examining open quantum systems, where we find several counterintuitive results that show that baths can, in some cases, enhance localization in certain systems, which may have use in realizing quantum computation.

We outline formal and physical similarities between the quantum dynamics of open systems, and the mesoscopic description of classical systems affected by weak noise. The main tool of our interest is the dissipative Wigner equation, that, for suitable timescales, becomes analogous to the Fokker-Planck equation describing classical advection and diffusion. This correspondence allows in principle to surmise a finite resolution, other than the Planck scale, for the quantized state space of the open system, particularly meaningful when the latter underlies chaotic classical dynamics. We provide representative examples of the quantum-stochastic parallel with noisy Hopf cycles and Van der Pol type oscillators., Comment: 14 pages, 6 figures

The paper investigates the quantum fluctuating dynamics by using the stochastic generalization of the Madelung quantum-hydrodynamic approach. By using the discrete approach, the path integral solution is derived in order to investigate how the final stationary configuration is obtained from the initial quantum superposition of states. The model shows that the quantum eigenstates remain stationary configurations with a very small perturbation of their mass density distribution and that any eigenstate, contributing to a quantum superposition of states, can be reached in the final stationary configuration. When the non-local quantum potential acquires a finite range of interaction, the work shows that the macroscopic coarse-grained description of the theory can lead to a really classical system. The minimum uncertainty attainable in the stochastic Madelung model is shown to be compatible with maximum speed of transmission of information and interactions. The theory shows that, in the quantum deterministic limit, the uncertainty relations of quantum mechanics are obtained. The connections with the decoherence theory and the Copenhagen interpretation of quantum mechanics are also discussed.

A magnetic field and temperature dependent quantum transport is investigated in a single molecular transistor. Our system is modelled by an onsite electron-electron correlation, polaronic interaction in the quantum dot and the coupling between quantum dot local phonon and the substrate phonon which produces a damping effect on the dynamics of the quantum dot. We use the Anderson-Holstein Hamiltonian along with the Caldeira-Leggett model to tackle the dissipation and polaronic effects and mean-field Hartree-Fock approximation to treat the onsite Coulomb correlation. We calculate transport properties such as spectral density function, tunnelling current, differential conductance employing finite-temperature Keldysh non-equilibrium Green function method under the influence of a finite temperature and an external magnetic field. It is shown that temperature has an intervening effect on the spin-resolved transport properties which can be used as a tuneable spin-filter.

The classical and quantum formulations for open systems related to dissipative dynamics are constructed on a complex hyperbolic ring, following universal symmetry principles, and considering the double thermal fields approach for modeling the system of interest, and the environment. The hyperbolic rotations are revealed as an underlying internal symmetry for the dissipative dynamics, and a chemical potential is identified as conjugate variable to the charge operator, and thus a grand partition function is constructed. As opposed to the standard scheme, there are not patologies associated with the existence of many unitarity inequivalent representations on the hyperbolic ring, since the whole of the dissipative quantum dynamics is realized by choosing only one representation of the field commutation relations. Entanglement entropy operators for the subsystem of interest and the environment, are constructed as a tool for study the entanglement generated from the dissipation. The holographic perspectives of our results are discussed., 30 pages, 2 figures

In this paper we discuss the temperature variation of a new chaotic optical field after it passes through a single-mode quantum dissipation and diffusion channel respectively. Using the entangled state representation and the technique of integration within ordered product (IWOP) of operators, we solve the master equations and obtain the new output fields. We show the final explicit forms of the new output fields by detailed derivation. By virtue of thermo dynamics theory at finite temperature, we finally conclude the results of temperature variation of chaotic optical field both in quantum dissipation channel and diffusion channel.

Accurate and efficient simulation on quantum dissipation with nonlinear environment couplings remains nowadays a challenging task. In this work, we propose to incorporate the stochastic fields, which resolve just the nonlinear environment coupling terms, into the dissipaton-equation-of-motion (DEOM) construction. The stochastic fields are introduced via the Hubbard-Stratonovich transformation. After the transformation, the resulted stochastic-fields-dressed total Hamiltonian contains only linear environment coupling terms. On basis of that, a stochastic-fields-dressed DEOM (SFD-DEOM) can then be constructed. The resultant SFD-DEOM, together with the ensemble average over the stochastic fields, constitutes an exact and nonperturbative approach to quantum dissipation under nonlinear environment couplings. It is also of relatively high efficiency and stability due to the fact that only nonlinear environment coupling terms are dealt with stochastic fields while linear couplings are still treated as the usual DEOM. Numerical demonstrations are carried out on a two-state model system., 7 pages, 5 figures (including 1 multimedia)

Singlet fission is believed to improve the efficiency of solar energy conversion by breaking up the Shockley-Queisser thermodynamic limit. Understanding of triplet excitons generated by singlet fission is essential for solar energy exploitation. Here we employed transient absorption microscopy to examine dynamical behaviors of triplet excitons. We observed anisotropic recombination of triplet excitons in hexacene single crystals. The triplet exciton relaxations from singlet fission proceed in both geminate and non-geminate recombination. For the geminate recombination, the different rates were attributed to the significant difference in their related energy change based on the Redfield quantum dissipation theory. The process is mainly governed by the electron-phonon interaction in hexacene. On the other hand, the non-geminate recombination is of bimolecular origin through energy transfer. In the triplet-triplet bimolecular process, the rates along the two different optical axes in the a-b crystalline plane differ by a factor of 4. This anisotropy in the triplet-triplet recombination rates was attributed to the interference in the coupling probability of dipole-dipole interactions in the different geometric configurations of hexacene single crystals. Our experimental findings provide new insight into future design of singlet fission materials with desirable triplet exciton exploitations.

A single molecular transistor is considered in the presence of electron-electron interaction, electron-phonon interaction, an external magnetic field and dissipation. The quantum transport properties of the system are investigated using the Anderson-Holstein Hamiltonian together with the Caldeira-Leggett model that takes care of the damping effect. The phonons are first removed from the theory by averaging the Hamiltonian with respect to a coherent phonon state and the resultant electronic Hamiltonian is finally solved with the help of the Green function technique due to Keldysh. The spectral function, spin-polarized current densities, differential conductance and spin polarization current are determined.

Summary Singlet fission is known to improve solar energy utilization by circumventing the Shockley-Queisser limit. The two essential steps of singlet fission are the formation of a correlated triplet pair and its subsequent quantum decoherence. However, the mechanisms of the triplet pair formation and decoherence still remain elusive. Here we examined both essential steps in single crystalline hexacene and discovered remarkable anisotropy of the overall singlet fission rate along different crystal axes. Since the triplet pair formation emerges on the same timescale along both crystal axes, the quantum decoherence is likely responsible for the directional anisotropy. The distinct quantum decoherence rates are ascribed to the notable difference on their associated energy loss according to the Redfield quantum dissipation theory. Our hybrid experimental/theoretical framework will not only further our understanding of singlet fission, but also shed light on the systematic design of new materials for the third-generation solar cells., Graphical Abstract, Highlights • Remarkable anisotropy of the overall singlet fission along different crystal axes • The correlated triplet pair emerges on the same timescale along both crystal axes • The quantum decoherence is predominantly driven by electron-phonon coupling • The anisotropic decoherence is due to the directional difference of its energy loss, Spectroscopy; Theoretical Photophysics; Quantum Phenomena

Understanding quantum dissipation is important from both theoretical perspective and applications. Here, we show how to describe dissipation in a scalar field theory. We treat dissipation non-perturbatively, represent it by a bilinear term in the Lagrangian and quantize the theory. We find that dissipation promotes a gap in momentum space and reduces the particle energy. As a result, particle mass becomes dressed by dissipation due to self-interaction. The underlying mechanism is similar to that governing the propagation of transverse collective modes in liquids. We discuss the interplay between the dissipative and mass terms, the associated different regimes of field dynamics and the emergence of ultraviolet and infrared cutoffs due to dissipation.

Orientador: Amir Ordacgi Caldeira Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin Resumo: Usamos o modelo "sistema-mais-reservatório" para estudar a dinâmica de um sistema de duas partículas que interagem com um reservatório em equilíbrio térmico, mas não interagem entre si. Apresentamos uma extensão do banho de osciladores capaz de induzir um acoplamento efetivo entre as partículas brownianas dependendo da escolha feita para a função espectral dos osciladores que compõem o banho. O acoplamento é não linear nas variáveis de interesse e impomos uma dependência exponencial nestas variáveis para garantir a invariância translacional do modelo. A interação efetiva resultante é apresentada usando as equações de movimento clágsicas e o limite quântico é estudado através do operador densidade reduzido das duas partículas. Mostramos que, no limite de tempos longos e distâncias curtas, o nosso modelo reproduz os resultados do modelo linear para o caso de apenas uma partícula. Finalmente, calculamos a evolução temporal de um estado inicial formado pelo produto de dois pacotes simples Abstract: We use the system-plus-reservoir model to study the dynamics of a system of two particles that interact with a heat bath in thermal equilibrium, but do not interact with each other. We present an extension of the bath of oscillators capable of inducing an effective coupling between the brownian particles depending on the choice made to the spectral function of the oscillators components of the bath. The coupling is non-linear in the variables of interest and an exponential dependence is imposed in order to guarantee the translational invariance of the model. The resultant effective interaction is presented using the classical equations of motion and the quantum limit is studied through the time evolution of reduced density operator of the two particles. We find that, in the limit of long times and short distances, our model reproduces the results of the linear model for the case of only one particle. Finally, we describe the time evolution of an initial state given by the product of two simple packets Mestrado Física da Matéria Condensada Mestre em Física

Dissipation in the quantum solid of graphene is couched in the methodology of nonequilibrium statistical mechanics of an open quantum system. Of specific interest is the absorption accompanied by relaxation of energy because of an external frequency-dependent oscillatory electric field. At optical frequencies and for sizable amplitude of the electric field, the response is nonlinear, the treatment of which is simplified by means of a ``rotating wave approximation'' in which rapidly changing, off-resonance terms are omitted. The characteristic resonant frequency is what quantifies the tunneling between the valence and the conduction bands across the so-called Dirac point in graphene. The valence and the conduction states are mapped into the eigenstates of pseudo Pauli spin operators and the corresponding Hamiltonian, when embedded in a dissipative heat bath comprising the surrounding phonons and other electrons, makes possible a comprehensive analysis in terms of the much-studied spin-boson model of dissipative quantum statistical mechanics. A master equation for the density operator associated with this Hamiltonian yields rate equations for the mean population of the valence and the conduction states as well as the transition (matrix elements) between them. Further approximation of these rate equations allows contact with phenomenological treatments of the nonlinear optical conductivity. The present paper then provides a microscopic framework for investigating the response characteristics of a material of great topical interest using contemporary methods of quantum dissipation.

In this work, we investigate the quantum phase transition of light in the dissipative Rabi-Hubbard lattice under the framework of the mean-field theory and quantum dressed master equation. The order parameter of photons in strong qubit-photon coupling regime is derived analytically both at zero and low temperatures. Interestingly, we can locate the localization and delocalization phase transition very well in a wide parameter region. {In particular for the zero-temperature limit, the critical tunneling strength approaches zero generally in the deep-strong qubit-photon coupling regime, regardless of the quantum dissipation. This is contrary to the previous results with the finite minimal critical tunneling strength based on the standard Lindblad master equation. Moreover, a significant improvement of the critical tunneling is also observed at finite temperature, compared with the counterpart under the Lindblad description. We hope these results may deepen the understanding of the phase transition of photons in the Rabi-Hubbard model., 7 pages, 1 figures

Orientador: Marcelo Moraes Guzzo Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin Resumo: Nesta tese, estudamos algumas consequências fenomenológicas da introdução do fenômeno de dissipação quântica na fenomenologia de oscilações de neutrinos em duas famílias. Utilizando a abordagem de equação mestra to tipo Lindblad-Kossakowski e o critério de completa positividade, descrevemos diferentes modelos para o sistema de oscilação de neutrinos sujeitos aos efeitos dissipativos causados por considerarmos que estes estão abertos a interagirem com o meio a seu redor. Investigamos como incluir os efeitos dissipativos para oscilação de neutrinos no vacuo e para quando os efeitos causados pelo potencial efetivo de matéria também estão incluídos no modelo de oscilação. Por m, aplicamos a fenomenologia estudada ao experimento MINOS como forma de observar como os efeitos dissipativos se comportam frente aos dados experimentais Abstract: In this thesis, we study the introduction of the quantum dissipation phenomenon and the phenomenological consequences in the model of neutrino oscillations in two families. Using the Lindblad-Kossakowski master-equation approach and the complete positivity condition, we describe different models for the neutrino oscillation system subject to dissipative effects, that are caused when we consider that neutrinos can interact with the environment around them, forming a open quantum system. We investigate as to include the dissipative e ects in neutrino oscillation in vacuum and when the effects of the efective potential of matter are also included in the model of oscillation. Finally, we apply the phenomenology studied to MINOS experiment as a way to observe the behavior of the dissipative e effects from experimental data Doutorado Física Doutor em Ciências

Quantum backaction from weak measurement affects the behavior of quantum systems. We consider a nonlinear driven Duffing oscillator system implementation in a nonlinear optical cavity, and we show that the choice of phase setting $\ensuremath{\phi}$ for a laser used in measurement can change the dissipation for the spread variables of the quantum state. This can considerably increase the energy absorbed via the energy channel of the spread variables and enhance quantum effects. This suggests novel applications to quantum control, as we demonstrate, including an example in which the energy in the spread variables allows for a dynamical tunneling between energetically separated dynamical stead-states.

We study quantum transport in a single molecular transistor in which the central region consists of a single-level quantum dot and is connected to two metallic leads that act as a source and a drain respectively. The quantum dot is considered to be under the influence of electron-electron and electron-phonon interactions. The central region is placed on an insulating substrate that acts as a heat reservoir that interacts with the quantum dot phonon giving rise to a damping effect to the quantum dot. The electron-phonon interaction is decoupled by applying a canonical transformation and then the spectral density of the quantum dot is calculated from the resultant Hamiltonian by using Keldysh Green function technique. We also calculate the tunneling current density and differential conductance to study the effect of quantum dissipation, electron correlation and the lattice effects on quantum transport in a single molecular transistor at finite temperature.

We provide a class of quantum evolution beyond Markovian semigroup. This class is governed by a hybrid Davies like generator such that dissipation is controlled by a suitable memory kernel and decoherence by standard GKLS generator. These two processes commute and both of them commute with the unitary evolution controlled by the systems Hamiltonian. The corresponding memory kernel gives rise to semi-Markov evolution of the diagonal elements of the density matrix. However, the corresponding evolution needs not be completely positive. The role of decoherence generator is to restore complete positivity. Hence, to pose the dynamical problem one needs two processes generated by classical semi-Markov memory kernel and purely quantum decoherence generator. This scheme is illustrated for a qubit evolution., 7 pages

We develop a non-Markovian approach to study quantum dissipation and thermal transport in the nonequilibrium two-level system based on a canonical transformation and full-counting statistics. Specifically, we analytically study dissipative dynamics of population difference, quantum coherence, and heat current in terms of the canonical transformed Redfield approach. It demonstrates that the dynamics of both the population difference and the energy flow show monotonic decaying behaviors with the identical decay rate, whereas the quantum coherence is dominated by the oscillation showing the non-Markovian effect. Moreover, through tuning the temperature bias of thermal baths, negative differential thermal conductance is clearly exhibited beyond the weak system-bath coupling limit and Markovian approximation. The results may provide guidance for the efficient control of energy and the information transport in nanodevices.

We consider an open quantum system with dissipation, described by a Lindblad Master equation (LME). For dissipation locally acting and sufficiently strong, a separation of the relaxation time scales occurs, which, in terms of the eigenvalues of the Liouvillian, implies a grouping of the latter in distinct vertical stripes in the complex plane at positions determined by the eigenvalues of the dissipator. We derive effective LME equations describing the modes within each stripe separately, and solve them perturbatively, obtaining for the full set of eigenvalues and eigenstates of the Liouvillian explicit expressions correct at order $1/\Gamma$ included, where $\Gamma$ is the strength of the dissipation. As a example, we apply our general results to quantum $XYZ$ spin chains coupled, at one boundary, to a dissipative bath of polarization., Comment: Letter + Supplemental Material

The decay of quantum vortex rings in counterflow regimes, visualized in Helium II with the help of solid hydrogen particles trapped to their cores, has been a puzzling issue within the usual description of superfluid vortex dynamics, grounded on the hypothesis that a vortex filament is, effectively, an extended massless object subject to a canceling superposition of Magnus and mutual friction forces. We discuss, from a general energy-budget point of view, a phenomenological solution of this problem, which relies on viscous and quantum dissipation mechanisms, the later associated to the backreaction of vortex singular structures on the surrounding two-component fluid mixture., Comment: 16 pages, 4 figures - one reference added + further clarifying comments on the Schwarz's description of vortex filament dynamics

This chapter is devoted to quantum mechanics fundamentals. The basic topics from quantum mechanics are covered including state vectors, operators, density operators and dynamics of a quantum system. We further describe quantum measurements, the uncertainty principle, and change of the basis. In addition, we describe harmonic oscillator, orbital angular momentum, spin-1/2 systems and hydrogen-like atoms. For deeper understanding of this material, a set of problems to be used for self study is provided.

In a fundamental formulation of the quantum mechanics of a closed system such as the universe as a whole, three forms of information are needed to make predictions for the probabilities of alternative time histories of the closed system . These are the action functional of the elementary particles, the quantum istate of the universe, and the description of our specific history. We discuss the origin of the "quasiclassical realm" of familiar experience and Hamiltonian quantum mechanics with its preferred time in such a formulation of quantum cosmology. It is argued that these features of the universe are not general properties of quantum theory, but rather approximate features that are emergent after the Planck time as a consequence of theories of the closed system's quantum state and dynamics., Comment: 23p, 4 figures, revtex4, history of ths article on title page. arXiv admin note: text overlap with arXiv:1805.12246