Arseni Goussev

University of Portsmouth · School of Mathematics and Physics

We address the phenomenon of diffraction of non-relativistic matter waves on openings in absorbing screens. To this end, we expand the full quantum propagator, connecting two points on the opposite sides of the screen, in terms of the free particle propagator and spatio-temporal properties of the opening. Our construction, based on the Huygens-Fres...

In the recent years, mater-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and study of fundamental aspects of quantum theory. Diffraction and interference of matter waves can be observed not only at a spatial aperture (such as a screen edge, slit, or grating), but also at a time-dom...

Quantum backflow is an interference effect in which a matter-wave packet comprised of only plane waves with non-negative momenta exhibits negative probability flux. Here we show that this effect is mathematically equivalent to the appearance of classically forbidden probability flux when a matter-wave packet, initially confined to a semi-infinite l...

In its original formulation, quantum backflow (QB) is an interference effect that manifests itself as a negative probability transfer for free-particle states comprised of plane waves with only positive momenta. Quantum reentry (QR) is another interference effect in which a wave packet expanding from a spatial region of its initial confinement part...

Free motion of a quantum particle with the wave function entirely comprised of plane waves with non-negative momenta may be accompanied by negative probability current, an effect called quantum backflow. The effect is weak and fragile and has not yet been observed experimentally. Here we show that quantum backflow becomes significantly more pronoun...

Quantum backflow refers to the counterintuitive fact that the probability can flow in the direction opposite to the momentum of a quantum particle. This phenomenon has been seen to be small and fragile for one-dimensional systems, in which the maximal amount of backflow has been found to be bounded. Quantum backflow exhibits dramatically different...

Quantum backflow refers to the counterintuitive fact that the probability can flow in the direction opposite to the momentum of a quantum particle. This phenomenon has been seen to be small and fragile for one-dimensional systems, in which the maximal amount of backflow has been found to be bounded. Quantum backflow exhibits dramatically different...

Comment on "Backflow in relativistic wave equations" by I. Bialynicki-Birula, Z. Bialynicka-Birula, and S. Augustynowicz [Journal of Physics A: Mathematical and Theoretical, volume 55, page 255702 (2022)].

Diffraction in time manifests itself as the appearance of probability-density fringes when a matter wave passes through an opaque screen with abrupt temporal variations of transmission properties. Here we analytically describe the phase-space structure of diffraction-in-time fringes for a class of smooth time gratings. More precisely, we obtain an...

Diffraction in time manifests itself as the appearance of probability-density fringes when a matter wave passes through an opaque screen with abrupt temporal variation of transmission properties. Here we analytically describe the phase-space structure of diffraction-in-time fringes for a class of smooth time gratings. More precisely, we obtain an a...

In its standard formulation, quantum backflow is a classically impossible phenomenon in which a free quantum particle in a positive-momentum state exhibits a negative probability current. Recently, Miller et al. [Quantum 5, 379 (2021)] have put forward a new, "experiment-friendly" formulation of quantum backflow that aims at extending the notion of...

In its standard formulation, quantum backflow is a classically impossible phenomenon in which a free quantum particle in a positive-momentum state exhibits a negative probability current. Recently, Miller et al. [Quantum 5, 379 (2021)] have put forward a new, "experiment-friendly" formulation of quantum backflow that aims at extending the notion of...

The left-to-right motion of a free quantum Gaussian wave packet can be accompanied by the right-to-left flow of the probability density, the effect recently studied by Villanueva. Using the Wigner representation of the wave packet, we analyze the effect in phase space and demonstrate that its physical origin is rooted in classical mechanics.

Free motion of a quantum wave packet comprised of only nonnegative-momentum plane waves may be accompanied by negative probability current, an effect called quantum backflow. The effect is weak when the wave packet motion takes place along a straight line: The backflow current at a fixed point in space integrated over a time window cannot exceed th...

The left-to-right motion of a free quantum Gaussian wave packet can be accompanied by the right-to-left flow of the probability density, the effect recently studied by Villanueva [Am. J. Phys. 88, 325 (2020)]. Using the Wigner representation of the wave packet, we analyze the effect in phase space, and demonstrate that its physical origin is rooted...

In its original formulation, quantum backflow (QB) is an interference effect that manifests itself as a negative probability transfer for free-particle states comprised of plane waves with only positive momenta. Quantum reentry (QR) is another interference effect in which a wave packet expanding from a spatial region of its initial confinement part...

We report the existence of a regime for domain-wall motion in uniaxial and near-uniaxial ferromagnetic nanowires, characterized by applied magnetic fields sufficiently strong that one of the domains becomes unstable. There appears a stable solution of the Landau-Lifshitz-Gilbert equation, describing a nonplanar domain wall moving with constant velo...

Quantum backflow is an interference effect in which a matter-wave packet comprised of only plane waves with non-negative momenta exhibits negative probability flux. Here we show that this effect is mathematically equivalent to the appearance of classically-forbidden probability flux when a matter-wave packet, initially confined to a semi-infinite l...

We report the existence of a new regime for domain wall motion in near-uniaxial ferromagnetic nanowires, characterised by applied magnetic fields sufficiently strong that one of the domains becomes unstable. There appears a new stable solution of the Landau-Lifshitz-Gilbert equation describing domain wall motion with characteristic velocity v and p...

There is no known exact expression for the propagator of a non-relativistic particle colliding with a hard sphere. De Prunel\'e (2008 {\it J.~Phys.~A:~Math.~Theor.} {\bf 41} 255305) derived a partial wave expansion of the propagator and compared it against some known approximations, including the semiclassical Van Vleck-Gutzwiller (VG) propagator;...

We propose the suppression of dispersive spreading of wave packets governed by the free-space Schrödinger equation with a periodically pulsed nonlinear term. Using asymptotic analysis, we construct stroboscopically dispersionless quantum states that are physically reminiscent of, but mathematically different from, the well-known one-soliton solutio...

We propose the suppression of dispersive spreading of wave packets governed by the free-space Schrödinger equation with a periodically pulsed nonlinear term. Using asymptotic analysis, we construct stroboscopically-dispersionless quantum states that are physically reminiscent of, but mathematically different from, the well-known one-soliton solutio...

We propose the suppression of dispersive spreading of wave packets governed by the free-space Schrödinger equation with a periodically pulsed nonlinear term. Using asymptotic analysis, we construct stroboscopically-dispersionless quantum states that are physically reminiscent of, but mathematically different from, the well-known one-soliton solutio...

We propose a method -- a quantum time mirror (QTM) -- for simulating a partial time-reversal of the free-space motion of a nonrelativistic quantum wave packet. The method is based on a short-time spatially-homogeneous perturbation to the wave packet dynamics, achieved by adding a nonlinear time-dependent term to the underlying Schr\"odinger equatio...

We address the time evolution of two- and three-dimensional nonrelativistic Gaussian wave packets in the presence of a weak external potential of arbitrary functional form. The focus of our study is the phenomenon of rotation of a Gaussian wave packet around its center of mass, as quantified by mean angular momentum computed relative to the wave pa...

We propose a method – a quantum time mirror (QTM) – for simulating the time-reversal of the free-space motion of Bose-Einstein condensate clouds as described by the nonlinear Schroedinger equation. The method is based on a short-time spatially-homogeneous perturbation to the cloud dynamics, achieved by externally modifying the strength of the inter...

Both metaphysical and practical considerations related to time inversion have intrigued scientists for generations. Physicists have strived to devise and implement time-inversion protocols, in particular different forms of "time mirrors" for classical waves. Here we propose an instantaneous time mirror for quantum systems, i.e., a controlled time d...

A ribbon is a surface swept out by a line segment turning as it moves along a central curve. For narrow magnetic ribbons, for which the length of the line segment is much less than the length of the curve, the anisotropy induced by the magnetostatic interaction is biaxial, with hard axis normal to the ribbon and easy axis along the central curve. T...

Echoes are ubiquitous phenomena in several branches of physics, ranging from acoustics, optics, condensed matter and cold atoms to geophysics. They are at the base of a number of very useful experimental techniques, such as nuclear magnetic resonance, photon echo and time-reversal mirrors. Particularly interesting physical effects are obtained when...

Both metaphysical and practical considerations related to time inversion have intrigued scientists for generations. Physicists have strived to devise and implement time-inversion protocols, in particular different forms of "time mirrors" for classical waves. Here we propose two conceptually different realisations of instantaneous time mirrors for q...

We present an analytic study of domain-wall statics and dynamics in ferromagnetic nanotubes with spin-orbit-induced Dzyaloshinskii-Moriya interaction (DMI). Even at the level of statics, dramatic effects arise from the interplay of space curvature and DMI: the domains become chirally twisted, leading to more compact domain walls. The dynamics of th...

We report a quantitative, analytical and numerical, comparison between two models of the interaction of a non-relativistic quantum particle with a thin time-dependent absorbing barrier. The first model represents the barrier by a set of time-dependent discontinuous matching conditions, which are closely related to Kottler boundary conditions used i...

A pulse of matter waves may dramatically change its shape when traversing an absorbing barrier with time-dependent transparency. Here we show that this effect can be utilized for controlled manipulation of spatially-localized quantum states. In particular, in the context of atom-optics experiments, we explicitly demonstrate how the proposed approac...

We address the time decay of the Loschmidt echo, measuring sensitivity of quantum dynamics to small Hamiltonian perturbations, in one-dimensional integrable systems. Using semiclassical analysis, we show that the Loschmidt echo may exhibit a well-pronounced regime of exponential decay, alike the one typically observed in quantum systems whose dynam...

We develop a systematic asymptotic description for domain wall motion in one-dimensional magnetic nanowires under the influence of small applied magnetic fields and currents and small material anisotropy. The magnetization dynamics, as governed by the Landau-Lifshitz-Gilbert equation, is investigated via a perturbation expansion. We compute leading...

Dynamics of magnetization domain walls (DWs) in thin ferromagnetic nanotubes subject to longitudinal external fields is addressed analytically in the regimes of strong and weak penalization. Explicit functional forms of the DW profiles and formulas for the DW propagation velocity are derived in both regimes. In particular, the DW speed is shown to...

We study the quantum Goos-Hänchen (GH) effect for wave-packet dynamics at a normal/superconductor (NS) interface. We find that the effect is amplified by a factor , with EF the Fermi energy and Δ the gap. Interestingly, the GH effect appears only as a time delay without any lateral shift, and the corresponding delay length is about , with the Fermi...

We consider the problem of quantum scattering of a localized wave packet by a weak Gaussian potential in two spatial dimensions. We show that, under certain conditions, this problem bears close analogy with that of focusing (or defocusing) of light rays by a thin optical lens: Quantum interference between straight paths yields the same lens equatio...

We study the quantum Goos-H\"{a}nchen(GH) effect for wave-packet dynamics at a normal/superconductor (NS) interface. We find that the effect is amplified by a factor $(E_F/\Delta)$, with $E_F$ the Fermi energy and $\Delta$ the gap. Interestingly, the GH effect appears only as a time delay $\delta t$ without any lateral shift, and the corresponding...

In this article we review the past, present, and future of the Loschmidt Echo.

It has recently been established that quantum statistics can play a crucial role in quantum escape. Here we demonstrate that boundary conditions can be equally important - moreover, in certain cases, may lead to a complete suppression of the escape. Our results are exact and hold for arbitrarily many particles.

Under a magnetic field along its axis, domain wall motion in a uniaxial nanowire is much slower than in the fully anisotropic case, typically by several orders of magnitude (the square of the dimensionless Gilbert damping parameter). However, with the addition of a magnetic field transverse to the wire, this behaviour is dramatically reversed; up t...

We show that recently reported precessing solution of Landau-Lifshitz-Gilbert equations in ferromagnetic nanowires is stable under small perturbations of initial data, applied field and anisotropy constant. Linear stability is established analytically, while nonlinear stability is verified numerically.

We study the short-time stability of quantum dynamics in quasi-one-dimensional systems with respect to small localized perturbations of the potential. To this end, we analytically and numerically address the decay of the Loschmidt echo (LE) during times that are short compared to the Ehrenfest time. We find that the LE is generally a nonmonotonic f...

We study fidelity decay in classically chaotic microwave billiards for a local, pistonlike boundary perturbation. We experimentally verify a predicted nonmonotonic crossover from the Fermi golden rule to the escape-rate regime of the Loschmidt echo decay with increasing local boundary perturbation. In particular, we observe pronounced oscillations...

The flux-flux correlation function formalism is a standard and widely used approach for the computation of reaction rates. In this paper we introduce a method to compute the classical and quantum flux-flux correlation functions for anharmonic barriers essentially analytically through the use of the classical and quantum normal forms. In the quantum...

Motivated by atomic optics experiments, we investigate a class of fidelity functions describing the reconstruction of quantum states by time-reversal operations as M(Da)(t) = vertical bar <psi vertical bar e(iH2t/2)e(iH1t/2)e(-iH2t/2)e(-iH1t/2)vertical bar psi >vertical bar(2). We show that the decay of M(Da) is quartic in time at short times and t...

Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the...

We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of normal form theory and the perspective of dynamical systems theory. Over the past ten years the classical normal form theory has provided a method for realizing the phase space structures that are responsible f...

We address the dynamics of magnetic domain walls in ferromagnetic nanowires under the influence of external time-dependent magnetic fields. We report a new exact spatiotemporal solution of the Landau-Lifshitz-Gilbert equation for the case of soft ferromagnetic wires and nanostructures with uniaxial anisotropy. The solution holds for applied fields...

Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the...

The quantum normal form approach to quantum transition state theory is used to compute the cumulative reaction probability for collinear exchange reactions. It is shown that for heavy-atom systems such as the nitrogen-exchange reaction, the quantum normal form approach gives excellent results and has major computational benefits over full reactive...

The Loschmidt echo (LE) (or fidelity) quantifies the sensitivity of the time evolution of a quantum system with respect to a perturbation of the Hamiltonian. In a typical chaotic system the LE has been previously argued to exhibit a long-time saturation at a value inversely proportional to the effective size of the Hilbert space of the system. Howe...

We address the decay in open chaotic quantum systems and calculate semiclassical corrections to the classical exponential decay. We confirm random matrix predictions and, going beyond, calculate Ehrenfest time effects. To support our results we perform extensive numerical simulations. Within our approach we show that certain (previously unnoticed)...

We address the sensitivity of quantum mechanical time evolution by considering the time decay of the Loschmidt echo (LE) (or fidelity) for local perturbations of the Hamiltonian. Within a semiclassical approach we derive analytical expressions for the LE decay for chaotic systems for the whole range from weak to strong local perturbations and ident...

We investigate the sensitivity of the time evolution of semiclassical wave packets in two-dimensional chaotic billiards with respect to local perturbations of their boundaries. For this purpose, we address, analytically and numerically, the time decay of the Loschmidt echo (LE). We find the LE to decay exponentially in time, with the rate equal to...

We consider the time evolution of a wave packet representing a quantum particle moving in a geometrically open billiard that consists of a number of fixed hard-disk or hard-sphere scatterers. Using the technique of multiple collision expansions we provide a first-principle analytical calculation of the time-dependent autocorrelation function for th...

Analysis of quantum dynamics in systems with classically chaotic analogs constitutes one of the main objectives for the field of Quantum Chaos. The quantum dynamics is known to be determined, to a large extent, by chaotic features of counterpart classical systems. We address time evolution of wave packets in open chaotic billiards, in which a quant...

This dissertation addresses the dynamics of a quantum particle moving in an array of fixed scatterers. The system is known as the Lorentz gas. The scatterers are taken to be two- or three-dimensional hard-spheres. The quantum Lorentz gas is analyzed in two dynamical regimes: (i) semiclassical regime, and (ii) high-energy diffraction regime. In both...

We consider the quantum-mechanical propagator for a particle moving in a d -dimensional Lorentz gas, with fixed, hard-sphere scatterers. To evaluate this propagator in the semiclassical region, and for times less than the Ehrenfest time, we express its effect on an initial Gaussian wave packet in terms of quantities analogous to those used to descr...

A novel universal (material-independent) negative differential resistance is shown to exist in strictly one-dimensional systems (quantum wires) as a consequence of energy and momentum conservation in the interaction of one-dimensional confined carriers with one-dimensional confined acoustic phonons. The average (steady state) carrier energy should...

Under proper conditions, small particles may be suspended in a regularly-spaced array called a Coulomb crystal. In this paper we discuss the application of this phenomenon to the self-assembly of nanoparticles in a lattice-lie array on a substrate. Issues associated with depositing the particles, and the size and lattice spacing of the particles ar...