arXiv subjects

Konstantin G. Zloshchastiev

Publications and source records attributed to Konstantin G. Zloshchastiev.

At least 37 records · Page 2Linked to original sources

arXiv2019

On the dynamical nature of nonlinear coupling of logarithmic quantum wave equation, Everett-Hirschman entropy and temperature

We study the dynamical behavior of nonlinear coupling in a quantum wave equation of a logarithmic type. Using statistical mechanical arguments for a large class of many-body systems, this coupling is shown to be related to temperature which is a thermodynamic conjugate to the Everett-Hirschman's quantum information entropy. A combined quantum-mechanical and field-theoretical model is proposed, which leads to a logarithmic equation with variable nonlinear coupling. We study its properties and present arguments regarding its nature and interpretation, including the connection to Landauer's principle. We also demonstrate that our model is able to describe linear quantum-mechanical systems with shape-changing external potentials.

quant-ph↗

arXiv2018

Stability and metastability of trapless Bose-Einstein condensates and quantum liquids

Various kinds of Bose-Einstein condensates are considered, which evolve without any geometric constraints or external trap potentials including gravitational. For studies of their collective oscillations and stability, including the metastability and macroscopic tunneling phenomena, both the variational approach and the Vakhitov-Kolokolov criterion are employed, calculations are done for condensates of an arbitrary spatial dimension. It is determined that that the trapless condensate described by the logarithmic wave equation is essentially stable, regardless of its dimensionality, while the trapless condensates described by wave equations of a polynomial type with respect to the wavefunction, such as the Gross-Pitaevskii (cubic), cubic-quintic, and so on, are at best metastable. This means that trapless "polynomial" condensates are unstable against spontaneous delocalization caused by fluctuations of their width, density and energy, leading to a finite lifetime.

cond-mat.quant-gas↗

arXiv2018

Sustainability of environment-assisted energy transfer in quantum photobiological complexes

It is shown that quantum sustainability is a universal phenomenon which emerges during environment-assisted electronic excitation energy transfer (EET) in photobiological complexes (PBCs), such as photosynthetic reaction centers and centers of melanogenesis. We demonstrate that quantum photobiological systems must be sustainable for them to simultaneously endure continuous energy transfer and keep their internal structure from destruction or critical instability. These quantum effects occur due to the interaction of PBCs with their environment which can be described by means of the reduced density operator and effective non-Hermitian Hamiltonian (NH). Sustainable NH models of EET predict the coherence beats, followed by the decrease of coherence down to a small, yet non-zero value. This indicates that in sustainable PBCs, quantum effects survive on a much larger time scale than the energy relaxation of an exciton. We show that sustainable evolution significantly lowers the entropy of PBCs and improves the speed and capacity of EET.

physics.bio-ph↗

arXiv2016

Singularity-free model of electrically charged fermionic particles and gauged Q-balls

We propose a model of an electrically charged fermion as a regular localized solution of electromagnetic and spinor fields interacting with a physical vacuum, which is phenomenologically described as a logarithmic superfluid. We analytically study the asymptotic behavior of the solution, while obtaining its form by numerical methods. The solution has physically plausible properties, such as finite size, self-energy, total charge and mass. In the case of spherical symmetry, its electric field obeys the Coulomb asymptotics at large distances from its core. It is shown that the observable rest mass of the fermion arises as a result of interaction of the fields with the physical vacuum. The spinor and scalar field components of the solution decay exponentially outside the core; therefore they can be regarded as internal degrees of freedom which can only be probed at sufficiently large scales of energy and momentum. Apart from conventional Fermi particles, our model can find applications in a theory of exotic localized objects, such as U(1) gauged Q-balls with half-integer spin.

hep-th↗

arXiv2016

Quantum-statistical approach to electromagnetic wave propagation and dissipation inside dielectric media and nanophotonic and plasmonic waveguides

Quantum-statistical effects occur during the propagation of electromagnetic (EM) waves inside the dielectric media or metamaterials, which include a large class of nanophotonic and plasmonic waveguides with dissipation and noise. Exploiting the formal analogy between the Schrodinger equation and the Maxwell equations for dielectric linear media, we rigorously derive the effective Hamiltonian operator which describes such propagation. This operator turns out to be essentially non-Hermitian in general, and pseudo-Hermitian in some special cases. Using the density operator approach for general non-Hermitian Hamiltonians, we derive a master equation that describes the statistical ensembles of EM wave modes. The method also describes the quantum dissipative and decoherence processes which happen during the wave's propagation, and, among other things, it reveals the conditions that are necessary to control the energy and information loss inside the above-mentioned materials.

physics.optics↗

arXiv2016

Quantum entropy of systems described by non-Hermitian Hamiltonians

We study the quantum entropy of systems that are described by general non-Hermitian Hamiltonians, including those which can model the effects of sinks or sources. We generalize the von Neumann entropy to the non- Hermitian case and find that one needs both the normalized and non-normalized density operators in order to properly describe irreversible processes. It turns out that such a generalization monitors the onset of disorder in quantum dissipative systems. We give arguments for why one can consider the generalized entropy as the informational entropy describing the flow of information between the system and the bath. We illustrate the theory by explicitly studying few simple models, including tunneling systems with two energy levels and non-Hermitian detuning.

quant-ph↗

arXiv2015

Non-Hermitian Hamiltonians and stability of pure states

We demonstrate that quantum fluctuations can cause, under certain conditions, the dynamical instability of pure states that can result in their evolution into mixed states. It is shown that the degree and type of such an instability are controlled by the environment-induced anti-Hermitian parts of Hamiltonians. Using the quantum-statistical approach for non-Hermitian Hamiltonians and related non-linear master equation, we derive the equations that are necessary to study the stability properties of any model described by a non-Hermitian Hamiltonian. It turns out that the instability of pure states is not preassigned in the evolution equation but arises as the emergent phenomenon in its solutions. In order to illustrate the general formalism and different types of instability that may occur, we perform the local stability analysis of some exactly solvable two-state models, which can be used in the theories of open quantum-optical and spin systems.

quant-ph↗

arXiv2015

Time correlation functions for non-Hermitian quantum systems

We introduce a formalism for time-dependent correlation functions for systems whose evolutions are governed by non-Hermitian Hamiltonians of general type. It turns out that one can define two different types of time correlation functions. Both these definitions seem to be physically consistent while becoming equivalent only in certain cases. Moreover, when autocorrelation functions are considered, one can introduce another function defined as the relative difference between the two definitions. We conjecture that such a function can be used to assess the positive semi-definiteness of the density operator without computing its eigenvalues. We illustrate these points by studying analytically a number of models with two energy levels.

quant-ph↗

arXiv2015

Non-Hamiltonian modeling of squeezing and thermal disorder in driven oscillators

Recently, model systems with quadratic Hamiltonians and time-dependent interactions were studied by Briegel and Popescu and by Galve et al. in order to consider the possibility of both quantum refrigeration in enzymes [Proc. R. Soc. 469 20110290 (2013)] and entanglement in the high temperature limit [Phys. Rev. Lett. 105 180501 (2010); Phys. Rev. A 81 062117 (2010)]. Following this line of research, we studied a model comprising two quantum harmonic oscillators driven by a time-dependent harmonic coupling. Such a system was embedded in a thermal bath represented in two different ways. In one case, the bath was composed of a finite but great number of independent harmonic oscillators with an Ohmic spectral density. In the other case, the bath was more efficiently defined in terms of a single oscillator coupled to a non-Hamiltonian thermostat. In both cases, we simulated the effect of the thermal disorder on the generation of the squeezed states in the two-oscillators relevant system. We found that, in our model, the thermal disorder of the bath determines the presence of a threshold temperature, for the generation of squeezed states, equal to T=311.13 K. Such a threshold is estimated to be within temperatures where chemical reactions and biological activity comfortably take place.

quant-ph↗

arXiv2014

Comparison and unification of non-Hermitian and Lindblad approaches with applications to open quantum optical systems

We compare two approaches to open quantum systems, namely, the non-Hermitian dynamics and the Lindblad master equation. In order to deal with more general dissipative phenomena, we propose the unified master equation that combines the characteristics of both of these approaches. This allows us to assess the differences between them as well as to clarify which observed features come from the Lindblad or the non-Hermitian part, when it comes to experiment. Using a generic two-mode single-atom laser system as a practical example, we analytically solve the dynamics of the normalized density matrix operator. We study the two-level model in a number of cases (depending on parameters and types of dynamics), compute different observables and study their physical properties. It turns out that one is able not only to describe the different types of damping in dissipative quantum optical systems but also to mimic the undamped anharmonic oscillatory phenomena which happen in quantum systems with more than two levels (while staying within the framework of the analytically simple two-mode approximation).

quant-ph↗

arXiv2013

Non-Hermitian quantum dynamics of a two-level system and models of dissipative environments

We consider a non-Hermitian Hamiltonian in order to effectively describe a two-level system coupled to a generic dissipative environment. The total Hamiltonian of the model is obtained by adding a general anti-Hermitian part, depending on four parameters, to the Hermitian Hamiltonian of a tunneling two-level system. The time evolution is formulated and derived in terms of the normalized density operator of the model, different types of decays are revealed and analyzed. In particular, the population difference and coherence are defined and calculated analytically. We have been able to mimic various physical situations with different properties, such as dephasing, vanishing population difference and purification.

quant-ph↗

arXiv2013

Singularity-free model of electric charge in physical vacuum: Non-zero spatial extent and mass generation

We propose a model of a spinless electrical charge as a self-consistent field configuration of the electromagnetic (EM) field interacting with a physical vacuum effectively described by the logarithmic quantum Bose liquid. We show that, in contrast to the EM field propagating in a trivial vacuum, a regular solution does exist, and both its mass and spatial extent emerge naturally from dynamics. It is demonstrated that the charge and energy density distribution acquire Gaussian-like form. The solution in the logarithmic model is stable and energetically favourable, unlike that obtained in a model with a quartic (Higgs-like) potential.

hep-th↗

arXiv2012

Volume element structure and roton-maxon-phonon excitations in superfluid helium beyond the Gross-Pitaevskii approximation

We propose a theory which deals with the structure and interactions of volume elements in liquid helium II. The approach consists of two nested models linked via parametric space. The short-wavelength part describes the interior structure of the fluid element using a non-perturbative approach based on the logarithmic wave equation; it suggests the Gaussian-like behaviour of the element's interior density and interparticle interaction potential. The long-wavelength part is the quantum many-body theory of such elements which deals with their dynamics and interactions. Our approach leads to a unified description of the phonon, maxon and roton excitations, and has noteworthy agreement with experiment: with one essential parameter to fit we reproduce at high accuracy not only the roton minimum but also the neighboring local maximum as well as the sound velocity and structure factor.

cond-mat.other↗

arXiv2011

Quantum Bose liquids with logarithmic nonlinearity: Self-sustainability and emergence of spatial extent

The Gross-Pitaevskii (GP) equation is a long-wavelength approach widely used to describe the dilute Bose-Einstein condensates (BEC). However, in many physical situations, such as higher densities, this approximation unlikely suffices hence one might need models which would account for long-range correlations and multi-body interactions. We show that the Bose liquid described by the logarithmic wave equation has a number of drastic differences from the GP one. It possesses the self-sustainability property: while the free GP condensate tends to spill all over the available volume the logarithmic one tends to form a Gaussian-type droplet - even in the absence of an external trapping potential. The quasi-particle modes of the logarithmic BEC are shown to acquire a finite size despite the bare particles being assumed point-like, i.e., the spatial extent emerges here as a result of quantum many-body correlations. Finally, we study the elementary excitations and demonstrate that the background density changes the topological structure of their momentum space which, in turn, affects their dispersion relations. Depending on the density the latter can be of the massive relativistic, massless relativistic, tachyonic and quaternionic type.

cond-mat.quant-gas↗

arXiv2011

Vacuum Cherenkov effect in logarithmic nonlinear quantum theory

We describe the radiation phenomena which can take place in the physical vacuum such as Cherenkov-type shock waves. Their macroscopical characteristics - cone angle, flash duration, radiation yield and spectral distribution - are computed. It turns out that the radiation yield is proportional to the square of the proper energy scale of the vacuum which serves also as the vacuum instability threshold and the natural ultraviolet cutoff. While the analysis is mainly based on the theory engaging the logarithmic nonlinear quantum wave equation, some of the obtained results must be valid for any Lorentz-invariance-violating theory describing the vacuum by (effectively) continuous medium in the long-wavelength approximation.

hep-th↗

arXiv2011

Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory

Our primary task is to demonstrate that the logarithmic nonlinearity in the quantum wave equation can cause the spontaneous symmetry breaking and mass generation phenomena on its own, at least in principle. To achieve this goal, we view the physical vacuum as a kind of the fundamental Bose-Einstein condensate embedded into the fictitious Euclidean space. The relation of such description to that of the physical (relativistic) observer is established via the fluid/gravity correspondence map, the related issues, such as the induced gravity and scalar field, relativistic postulates, Mach's principle and cosmology, are discussed. For estimate the values of the generated masses of the otherwise massless particles such as the photon, we propose few simple models which take into account small vacuum fluctuations. It turns out that the photon's mass can be naturally expressed in terms of the elementary electrical charge and the extensive length parameter of the nonlinearity. Finally, we outline the topological properties of the logarithmic theory and corresponding solitonic solutions.

hep-ph↗

arXiv2010

Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences

Starting from a generic generally covariant classical theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra governed by this non-linear correction. It turns out that such time parametrization is essentially energy-dependent and becomes global only asymptotically - when the energies get very small comparing to the effective quantum gravity scale. Similar thing happens to the Lorentz invariance - in the resulting theory it becomes an asymptotic low-energy phenomenon. We show how the logarithmic non-linearity deforms the vacuum wave dispersion relations and explains certain features of the astrophysical data coming from recent observations of high-energy cosmic rays. In general, the estimates imply that ceteris paribus the particles with higher energy propagate slower than those with lower one, therefore, for a high-energy particle the mean free path, lifetime in a high-energy state and, therefore, travel distance from the source can be significantly larger than one would expect from the conventional theory. Apart from this, we discuss also the possibility and conditions of the transluminal phenomena in the physical vacuum such as the Cherenkov-type shock waves.

hep-th↗

arXiv2009

Comment on "A limit on the variation of the speed of light arising from quantum gravity effects" aka "Testing Einstein's special relativity with Fermi's short hard gamma-ray burst GRB090510"

Recently the Fermi GBM and LAT Collaborations reported their new observational data disfavoring quite a number of the quantum gravity theories, including the one suggesting the nonlinear (logarithmic) modification of a quantum wave equation. We show that the latter is still far from being ruled out: it is not only able to explain the new data but also its phenomenological implications turn out to be more vast (and more interesting) than one expected before.

physics.gen-ph↗