arXiv subjects

Denys I. Bondar

Publications and source records attributed to Denys I. Bondar.

At least 91 records · Page 5Linked to original sources

arXiv2017

No thermalization without correlations

The proof of the long-standing conjecture is presented that Markovian quantum master equations are at odds with quantum thermodynamics under conventional assumptions of fluctuation-dissipation theorems (implying a translation invariant dissipation). Specifically, except for identified systems, persistent system-bath correlations of at least one kind, spatial or temporal, are obligatory for thermalization. A systematic procedure is proposed to construct translation invariant bath models producing steady states that well-approximate thermal states. A quantum optical scheme for the laboratory assessment of the developed procedure is outlined.

quant-ph↗

arXiv2017

Analytic Solutions to Coherent Control of the Dirac Equation

A simple framework for Dirac spinors is developed that parametrizes admissible quantum dynamics and also analytically constructs electromagnetic fields, obeying Maxwell's equations, which yield a desired evolution. In particular, we show how to achieve dispersionless rotation and translation of wave packets. Additionally, this formalism can handle control interactions beyond electromagnetic. This work reveals unexpected flexibility of the Dirac equation for control applications, which may open new prospects for quantum technologies.

quant-ph↗

arXiv2017

Making Distinct Dynamical Systems Appear Spectrally Identical

We show that a laser pulse can always be found that induces a desired optical response from an arbitrary dynamical system. As illustrations, driving fields are computed to induce the same optical response from a variety of distinct systems (open and closed, quantum and classical). As a result, the observed induced dipolar spectra without detailed information on the driving field is not sufficient to characterize atomic and molecular systems. The formulation may also be applied to design materials with specified optical characteristics. These findings reveal unexplored flexibilities of nonlinear optics.

quant-ph↗

arXiv2016

Quantum friction: environment engineering perspectives

We prove a generalization of the Lindblad's fundamental no-go result: A quantum system cannot be completely frozen and, in some cases, even thermalized via translationally invariant dissipation -- the quantum friction. Nevertheless, a practical methodology is proposed for engineering nearly perfect quantum analogs of classical friction within the Doppler cooling framework. These findings pave the way for hallmark dissipative engineering (e.g. nonreciprocal couplings) with atoms and molecules.

quant-ph↗

arXiv2016

Dirac open quantum system dynamics: formulations and simulations

We present an open system interaction formalism for the Dirac equation. Overcoming a complexity bottleneck of alternative formulations, our framework enables efficient numerical simulations (utilizing a typical desktop) of relativistic dynamics within the von Neumann density matrix and Wigner phase space descriptions. Employing these instruments, we gain important insights into the effect of quantum dephasing for relativistic systems in many branches of physics. In particular, the conditions for robustness of Majorana spinors against dephasing are established. Using the Klein paradox and tunneling as examples, we show that quantum dephasing does not suppress negative energy particle generation. Hence, the Klein dynamics is also robust to dephasing.

quant-ph↗

arXiv2016

Efficient computations of quantum canonical Gibbs state in phase space

The Gibbs canonical state, as a maximum entropy density matrix, represents a quantum system in equilibrium with a thermostat. This state plays an essential role in thermodynamics and serves as the initial condition for nonequilibrium dynamical simulations. We solve a long standing problem for computing the Gibbs state Wigner function with nearly machine accuracy by solving the Bloch equation directly in the phase space. Furthermore, the algorithms are provided yielding high quality Wigner distributions for pure stationary states as well as for Thomas-Fermi and Bose-Einstein distributions. The developed numerical methods furnish a long-sought efficient computation framework for nonequilibrium quantum simulations directly in the Wigner representation.

quant-ph↗

arXiv2016

Wigner-Lindblad equations for quantum friction

Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings significantly advance a long search for a universally valid Lindblad model of quantum friction and open opportunities for exploring novel dissipation phenomena.

quant-ph↗

arXiv2015

Efficient method to generate time evolution of the Wigner function for open quantum systems

The Wigner function is a useful tool for exploring the transition between quantum and classical dynamics, as well as the behavior of quantum chaotic systems. Evolving the Wigner function for open systems has proved challenging however; a variety of methods have been devised but suffer from being cumbersome and resource intensive. Here we present an efficient fast-Fourier method for evolving the Wigner function, that has a complexity of $O(N\log N)$ where $N$ is the size of the array storing the Wigner function. The efficiency, stability, and simplicity of this method allows us to simulate open system dynamics previously thought to be prohibitively expensive. As a demonstration we simulate the dynamics of both one-particle and two-particle systems under various environmental interactions. For a single particle we also compare the resulting evolution with that of the classical Fokker-Planck and Koopman-von Neumann equations, and show that the environmental interactions induce the quantum-to-classical transition as expected. In the case of two interacting particles we show that an environment interacting with one of the particles leads to the loss of coherence of the other.

quant-ph↗

arXiv2015

Excess of positrons in cosmic rays: A Lindbladian model of quantum electrodynamics

The fraction of positrons and electrons in cosmic rays recently observed on the International Space Station unveiled an unexpected excess of the positrons, undermining the current foundations of cosmic rays sources. We provide a quantum electrodynamics phenomenological model explaining the observed data. This model incorporates electroproduction, in which cosmic ray electrons decelerating in the interstellar medium emit photons that turn into electron-positron pairs. These findings not only advance our knowledge of cosmic ray physics, but also pave the way for computationally efficient formulations of quantum electrodynamics, critically needed in physics and chemistry.

physics.gen-ph↗

arXiv2014

Non-classicality of positive relativistic Wigner function

In nonrelativistic quantum mechanics, Hudsons theorem states that a Gaussian wavefunction is the only pure state corresponding to a positive Wigner function (WF). We explicitly construct non Gaussian Dirac spinors with positive relativistic WF. These pure states are coherent superpositions of particles and antiparticles, while the existence of positive WF exclusive composed of particles is conjectured. These observations challenge a common belief that states with positive WF are classical or have classical analogues, and may open new venues in relativistic quantum information.

quant-ph↗

arXiv2013

Wigner phase space distribution as a wave function

We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a certain point of the classical phase space. Additionally, we establish that in the classical limit, the Wigner function transforms into a classical Koopman-von Neumann wave function rather than into a classical probability distribution. Since probability amplitude need not be positive, our findings provide an alternative outlook on the Wigner function's negativity.

quant-ph↗

arXiv2013

Conceptual inconsistencies in finite-dimensional quantum and classical mechanics

Utilizing operational dynamic modeling [Phys. Rev. Lett. 109, 190403 (2012); arXiv:1105.4014], we demonstrate that any finite-dimensional representation of quantum and classical dynamics violates the Ehrenfest theorems. Other peculiarities are also revealed, including the nonexistence of the free particle and ambiguity in defining potential forces. Non-Hermitian mechanics is shown to have the same problems. This work compromises a popular belief that finite-dimensional mechanics is a straightforward discretization of the corresponding infinite-dimensional formulation.

quant-ph↗

arXiv2013

Operational Dynamic Modeling Transcending Quantum and Classical Mechanics

We introduce a general and systematic theoretical framework for Operational Dynamic Modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.

quant-ph↗

arXiv2012

NMR quantum gate factorization through canonical cosets

The block canonical coset decomposition is developed as a universal algorithmic tool to synthesize n-qubit quantum gates out of experimentally realizable NMR elements. The two-, three-, and four-qubit quantum Fourier transformations are worked out as examples. The proposed decomposition bridges the state of the art numerical analysis with NMR quantum gate synthesis.

quant-ph↗

arXiv2012

Relativistic Wigner function and consistent classical limit for spin 1/2 particles

The relativistic Wigner function for spin 1/2 particles is the subject of active research due to diverse applications. However, further progress is hindered by the fabulous complexity of the integro-differential equations of motion. We simplify these equations to partial differential equations of the Dirac type that are not only well suited for numerical computation, but also posses a well defined classical limit in a manifestly covariant form.

quant-ph↗

arXiv2011

Shapes of leading tunnelling trajectories for single-electron molecular ionization

Based on the geometrical approach to tunnelling by P.D. Hislop and I.M. Sigal [Memoir. AMS 78, No. 399 (1989)], we introduce the concept of a leading tunnelling trajectory. It is then proven that leading tunnelling trajectories for single-active-electron models of molecular tunnelling ionization (i.e., theories where a molecular potential is modelled by a single-electron multi-centre potential) are linear in the case of short range interactions and "almost" linear in the case of long range interactions. The results are presented on both the formal and physically intuitive levels. Physical implications of the obtained results are discussed.

physics.atom-ph↗

arXiv2011

Quantum mechanics of a free particle from properties of the Dirac delta function

Based on the assumption that the probability density of finding a free particle is independent of position, we infer the form of the eigenfunction for the free particle, $\bra{x} p > = \exp(ipx/\hbar)/\sqrt{2π\hbar}$. The canonical commutation relation between the momentum and position operators and the Ehrenfest theorem in the free particle case are derived solely from differentiation of the delta function and the form of $\bra{x} p >$.

math-ph↗

arXiv2010

The reproduction of the dynamics of a quantum system by an ensemble of classical particles beyond de Broglie--Bohmian mechanics

It is shown that for any given quantum system evolving unitarily with the Hamiltonian, $\hat{H} = \hat{\bf p}^2/(2m) + U({\bf q})$, [bold letters denote $D$-dimensional ($D \geqslant 3$) vectors] and with a sufficiently smooth potential $U({\bf q})$, there exits a classical ensemble with the Hamilton function, $\mathrsfs{H} ({\bf p}, {\bf q}) = {\bf p}^2/(2m) + U^{(\infty)} ({\bf q})$, where the potential $U^{(\infty)}({\bf q})$ coincides with $U({\bf q})$ for almost all ${\bf q}$ (i.e., $U^{(\infty)}$ can be different from $U$ only on a measure zero set), such that the square modulus of the wave function in the coordinate (momentum) representation approximately equals the coordinate (momentum) distribution of the classical ensemble within an arbitrary given accuracy. Furthermore, the trajectories of this classical ensemble, generally speaking, need not coincide with the trajectories obtained from de Broglie--Bohmian mechanics. Consequences of this result are discussed.

quant-ph↗