Theory Of Quantum Systems Research Articles

Non-Hermitian linear-response theory for spin diffusion in quantum systems

Spin transport theory of non-Hermitian quantum systems, where the non-Hermiticity led to a series of exotic phenomena when the system experiences dissipation to an environment is proposed. The goal is a better understanding of the spin diffusion in the one-dimensional non-Hermitian XXZ model which allows the transport coefficients be computed analytically. Moreover, we analyzed the electric transport in the one-dimensional non-Hermitian Hubbard model which is a very important model of electrons strongly correlated, where we have investigated the effect of non-Hermitian parameters like the imaginary hopping on AC and DC conductivities of the system. We analyzed the large U limit of this model, where such non-Hermiticity contributes with a minus sign in the virtual exchange of quasiparticles and the behavior of the ground state energy and low-lying excitations is reversed.

Microscopic Derivation of Transition-state Theory for Complex Quantum Systems

Microscopic Derivation of Transition-state Theory for Complex Quantum Systems

On spectral and scattering theory for one-body quantum systems in crossed constant electric and magnetic fields

In this paper, we study the spectral and scattering theory on the Hamiltonians which govern one-body quantum systems in crossed constant electric and magnetic fields. As one of the spectral features of the Hamiltonians, we show the absence of bound states of theirs under some appropriate conditions on the potentials. Moreover, by using the limiting absorption principle for the Hamiltonians, we give a simplified proof of the asymptotic completeness in short-range scattering.

Complex semiclassical theory for non-Hermitian quantum systems

Complex semiclassical theory for non-Hermitian quantum systems

Perturbation theory for the logarithm of a positive operator

In various contexts in mathematical physics, such as out-of-equilibrium physics and the asymptotic information theory of many-body quantum systems, one needs to compute the logarithm of a positive unbounded operator. Examples include the von Neumann entropy of a density matrix and the flow of operators with the modular Hamiltonian in the Tomita-Takesaki theory. Often, one encounters the situation where the operator under consideration, which we denote by ∆, can be related by a perturbative series to another operator ∆0, whose logarithm is known. We set up a perturbation theory for the logarithm log ∆. It turns out that the terms in the series possess a remarkable algebraic structure, which enables us to write them in the form of nested commutators plus some “contact terms”.

A Local Approach to the Theory of Open Optical Quantum Systems and “Violation” of the Second Law of Thermodynamics

A Local Approach to the Theory of Open Optical Quantum Systems and “Violation” of the Second Law of Thermodynamics

Equivalent quantum systems

We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects the Hamiltonian operators associated with each quantum system. This bridge allows us to connect different quantum systems, in such a way that studying one of them allows to understand the other through a gauge transformation. Furthermore, we included the case where the Hamiltonian operator can be time-dependent. An application for this construction will be achieved in the theory of control quantum systems.

ON THE METAPHYSICS OF QUANTUM ENTANGLEMENT

Concept of quantum entanglement, its role in physics, philosophy, and in updating general worldview are studied in this article. It is pointed out that Schrodinger introduced this concept and some derivatives from it into description of physical reality in the 1935 article in the context of discussion around the Einstein-Podolsky-Rosen thought experiment, but in the related 1936 publication he did not use them. Taking into account the concepts of a mixture and statistical operator, which were introduced by von Neumann and borrowed by Schrödinger, it is shown that the concept of entanglement is not necessary in quantum mechanics unconditionally. At a certain moment of development of the complex quantum systems theory, this concept and its derivatives served as not very successful substitutes for the concepts of a mixture, situation of a mixture. Comparative analysis of some Schrödinger’s, von Neumann’s, and Landau’s theoretical works concludes that imagination of a complex quantum system as a quasi-mechanical aggregate was gradually being overcome; its objective wholeness was being substantiated instead. Therefore, wholeness is inherent not only to quantum phenomena, but also to quantum systems by itself, objectively. By the essence, just the attempt to think this circumstance had brought into life the concept of quantum entanglement. The concept of a mixture and its substitutes – the concepts of entangled state, entanglement, etc. – have not only the scientific but some metaphysical meaning as well: they prove the possibility of rational thinking of wholeness, the reasonableness and effectiveness of rational holism. Therefore, the metaphysics of quantum entanglement in its correct understanding is a manifestation of the rational holism metaphysics. Complete explanation of the Einstein-Podolsky-Rosen thought experiment requires consideration of both these appearances of the quantum wholeness. One can say the essential result of long-term discussion of the EPR experiment is the exhaustive recognition of the quantum reality wholeness. A row of generalizations achieved by A. Alexandrov, I. Tsekhmistro, and D.Bohm are considered. Together with the completed study of the concept of quantum entanglement or Bohr's substantiation of the concept of undivided quantum phenomenon, they support irreducibility of physical reality, the Universe in general to any set of Democritian atoms and their countless combinations, aggregates. All this enriches and improves the understanding of the Universe as a real wholeness. Perhaps, this understanding will be newest substitution for the hitherto popular worldview in the spirit of Democritus.

Mutual friction and diffusion of two-dimensional quantum vortices

We present a microscopic open quantum systems theory of thermally-damped vortex motion in oblate atomic superfluids that includes previously neglected energy-damping interactions between superfluid and thermal atoms. This mechanism couples strongly to vortex core motion and causes dissipation of vortex energy due to mutual friction, as well as Brownian motion of vortices due to thermal fluctuations. We derive an analytic expression for the dimensionless mutual friction coefficient that gives excellent quantitative agreement with experimentally measured values, without any fitted parameters. Our work closes an existing two orders of magnitude gap between dissipation theory and experiments, previously bridged by fitted parameters, and provides a microscopic origin for the mutual friction and diffusion of quantized vortices in two-dimensional atomic superfluids.

Optomechanical effects in nanocavity-enhanced resonant Raman scattering of a single molecule

In this article, we address the optomechanical effects in surface-enhanced resonant Raman scattering (SERRS) from a single molecule in a nano-particle on mirror (NPoM) nanocavity by developing a quantum master equation theory, which combines macroscopic quantum electrodynamics and electron-vibration interaction within the framework of open quantum system theory. We supplement the theory with electromagnetic simulations and time-dependent density functional theory calculations in order to study the SERRS of a methylene blue molecule in a realistic NPoM nanocavity. The simulations allow us not only to identify the conditions to achieve conventional optomechanical effects, such as vibrational pumping, non-linear scaling of Stokes and anti-Stokes scattering, but also to discovery distinct behaviors, such as the saturation of exciton population, the emergence of Mollow triplet side-bands, and higher-order Raman scattering. All in all, our study might guide further investigations of optomechanical effects in resonant Raman scattering.

Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with U(1) symmetry

We study a ($1+1$)-dimensional quantum circuit consisting of Haar-random unitary gates and projective measurements, both of which conserve a total $U(1)$ charge and thus have $U(1)$ symmetry. In addition to a measurement-induced entanglement transition between a volume-law and an area-law entangled phase, we find a phase transition between two phases characterized by bipartite charge fluctuation growing with the subsystem size or staying constant. At this charge-fluctuation transition, steady-state quantities obtained by evolving an initial state with a definitive total charge exhibit critical scaling behaviors akin to Tomonaga-Luttinger-liquid theory for equilibrium critical quantum systems with $U(1)$ symmetry, such as logarithmic scaling of bipartite charge fluctuation, power-law decay of charge correlation functions, and logarithmic scaling of charge-resolved entanglement whose coefficient becomes a universal quadratic function in a flux parameter. These critical features, however, do not persist below the transition, in contrast to a recent prediction based on replica field theory and mapping to a classical statistical mechanical model.

Combining experiments on luminescent centres in hexagonal boron nitride with the polaron model and ab initio methods towards the identification of their microscopic origin.

The two-dimensional material hexagonal boron nitride (hBN) hosts luminescent centres with emission energies of ∼2 eV which exhibit pronounced phonon sidebands. We investigate the microscopic origin of these luminescent centres by combining ab initio calculations with non-perturbative open quantum system theory to study the emission and absorption properties of 26 defect transitions. Comparing the calculated line shapes with experiments we narrow down the microscopic origin to three carbon-based defects: C2CB, C2CN, and VNCB. The theoretical method developed enables us to calculate so-called photoluminescence excitation (PLE) maps, which show excellent agreement with our experiments. The latter resolves higher-order phonon transitions, thereby confirming both the vibronic structure of the optical transition and the phonon-assisted excitation mechanism with a phonon energy ∼170 meV. We believe that the presented experiments and polaron-based method accurately describe luminescent centres in hBN and will help to identify their microscopic origin.

A Schmidt Decomposition Approach to Quantum Thermodynamics.

The development of a self-consistent thermodynamic theory of quantum systems is of fundamental importance for modern physics. Still, despite its essential role in quantum science and technology, there is no unifying formalism for characterizing the thermodynamics within general autonomous quantum systems, and many fundamental open questions remain unanswered. Along these lines, most current efforts and approaches restrict the analysis to particular scenarios of approximative descriptions and semi-classical regimes. Here, we propose a novel approach to describe the thermodynamics of arbitrary bipartite autonomous quantum systems based on the well-known Schmidt decomposition. This formalism provides a simple, exact, and symmetrical framework for expressing the energetics between interacting systems, including scenarios beyond the standard description regimes, such as strong coupling. We show that this procedure allows straightforward identification of local effective operators suitable for characterizing the physical local internal energies. We also demonstrate that these quantities naturally satisfy the usual thermodynamic notion of energy additivity.

Generalized hydrodynamics of the KdV soliton gas

We establish the explicit correspondence between the theory of soliton gases in classical integrable dispersive hydrodynamics, and generalized hydrodynamics (GHD), the hydrodynamic theory for many-body quantum and classical integrable systems. This is done by constructing the GHD description of the soliton gas for the Korteweg–de Vries equation. We further predict the exact form of the free energy density and flux, and of the static correlation matrices of conserved charges and currents, for the soliton gas. For this purpose, we identify the solitons’ statistics with that of classical particles, and confirm the resulting GHD static correlation matrices by numerical simulations of the soliton gas. Finally, we express conjectured dynamical correlation functions for the soliton gas by simply borrowing the GHD results. In principle, other conjectures are also immediately available, such as diffusion and large-deviation functions for fluctuations of soliton transport.

Microscopic and macroscopic effects in the decoherence of neutrino oscillations

We present a generic structure (the layer structure) for decoherence effects in neutrino oscillations, which includes decoherence from quantum mechanical and classical uncertainties. The calculation is done by combining the concept of open quantum system and quantum field theory, forming a structure composed of phase spaces from microscopic to macroscopic level. Having information loss at different levels, quantum mechanical uncertainties parameterize decoherence by an intrinsic mass eigenstate separation effect, while decoherence for classical uncertainties is typically dominated by a statistical averaging effect. With the help of the layer structure, we classify the former as state decoherence (SD) and the latter as phase decoherence (PD), then further conclude that both SD and PD result from phase wash-out effects of different phase structures on different layers. Such effects admit for simple numerical calculations of decoherence for a given width and shape of uncertainties. While our structure is generic, so are the uncertainties, nonetheless, a few notable ones are: the wavepacket size of the external particles, the effective interaction volume at production and detection, the energy reconstruction model and the neutrino production profile. Furthermore, we estimate the experimental sensitivities for SD and PD parameterized by the uncertainty parameters, for reactor neutrinos and decay-at-rest neutrinos, using a traditional rate measuring method and a novel phase measuring method.

Toward exact predictions of spin-phonon relaxation times: An ab initio implementation of open quantum systems theory.

Spin-phonon coupling is the main driver of spin relaxation and decoherence in solid-state semiconductors at finite temperature. Controlling this interaction is a central problem for many disciplines, ranging from magnetic resonance to quantum technologies. Spin relaxation theories have been developed for almost a century but often use a phenomenological description of phonons and their coupling to spin, resulting in a nonpredictive tool and hindering our detailed understanding of spin dynamics. Here, we combine time-local master equations up to the fourth order with advanced electronic structure methods and perform predictions of spin-phonon relaxation time for a series of solid-state coordination compounds based on both transition metals and lanthanide Kramers ions. The agreement between experiments and simulations demonstrates that an accurate, universal, and fully ab initio implementation of spin relaxation theory is possible, thus paving the way to a systematic study of spin-phonon relaxation in solid-state materials.

Few-particle scattering from localized quantum systems in spatially structured bosonic baths

Understanding dynamics of localized quantum systems embedded in engineered bosonic environments is a central problem in quantum optics and open quantum system theory. We present a formalism for studying few-particle scattering from a localized quantum system interacting with an bosonic bath described by an inhomogeneous wave-equation. In particular, we provide exact relationships between the quantum scattering matrix of this interacting system and frequency domain solutions of the inhomogeneous wave-equation thus providing access to the spatial distribution of the scattered few-particle wave-packet. The formalism developed in this paper paves the way to computationally understanding the impact of structured media on the scattering properties of localized quantum systems embedded in them without simplifying assumptions on the physics of the structured media.

Symmetry aspects of chiral superconductors

Recent developments in theory, synthesis, and experimental probes of quantum systems have revealed many suitable candidate materials to host chiral superconductivity. Chiral superconductors are a subset of unconventional superconductors which break time-reversal symmetry. Time-reversal symmetry breaking is possible given the order parameter's two-component nature, allowing for a complex relative phase. In this article, we focus on discussing the underlying symmetry aspects that allow for the development of chiral superconductivity. We provide an introductory account of key concepts in group theory and apply these to the classification of order parameters and the generalization of the Landau theory of phase transitions in the context of superconductivity.

Theory of multiple quantum coherence signals in dilute thermal gases

Manifestations of dipole–dipole interactions in dilute thermal gases are difficult to sense because of strong inhomogeneous broadening. Recent experiments reported signatures of such interactions in fluorescence detection-based measurements of multiple quantum coherence (MQC) signals, with many characteristic features hitherto unexplained. We develop an original open quantum systems theory of MQC in dilute thermal gases, which allows us to resolve this conundrum. Our theory accounts for the vector character of the atomic dipoles as well as for driving laser pulses of arbitrary strength, includes the far-field coupling between the dipoles, which prevails in dilute ensembles, and effectively incorporates atomic motion via a disorder average. We show that collective decay processes—which were ignored in previous treatments employing the electrostatic form of dipolar interactions—play a key role in the emergence of MQC signals.

Nonequilibrium Work Relations and Response Theories in Ensemble Quantum Systems.

We develop a nonequilibrium response theory for macroscopic quantum systems that separates the contributions of ensemble heterogeneity and intrinsic quantum uncertainty. To accomplish this, we describe systems with a quantum P-ensemble, which goes beyond the standard density matrix description by explicitly specifying the classical heterogeneity between individual quantum systems in an ensemble. We use the P-ensemble formalism to present quantum generalizations of linear response theory and the Jarzynski nonequilibrium work relation. We derive these generalizations from a Bochkov-Kuzovlev generating functional for quantum P-ensembles, which can be further utilized to derive all orders of response theory that apply to ensemble quantum systems. We contrast these developments with their ρ-ensemble analogs, and we discuss how these P-ensemble theories provide a guide for an effective application of single molecule experiments.