arXiv subjects

Arseni Goussev

Publications and source records attributed to Arseni Goussev.

48 records · Page 3Linked to original sources

arXiv2010

Long-Time Coherence in Echo Spectroscopy with $π/2$--$π$--$π/2$ Pulse Sequence

Motivated by atom optics experiments, we investigate a new class of fidelity functions describing the reconstruction of quantum states by time-reversal operations as $M_{\mathrm{Da}}(t) = | <ψ| e^{i H_2 t / 2} e^{i H_1 t / 2} e^{-i H_2 t / 2} e^{-i H_1 t / 2} | ψ>|^2$. We show that the decay of $M_{\mathrm{Da}}$ is quartic in time at short times, and that it freezes well above the ergodic value at long times, when $H_2-H_1$ is not too large. The long-time saturation value of $M_{\mathrm{Da}}$ contains easily extractable information on the strength of decoherence in these systems.

quant-ph↗

arXiv2010

The Flux-Flux Correlation Function for Anharmonic Barriers

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 case we show that the quantum normal form reduces the computation of the flux-flux correlation function to that of an effective one dimensional anharmonic barrier. The example of the computation of the quantum flux-flux correlation function for a fourth order anharmonic barrier is worked out in detail, and we present an analytical expression for the quantum mechanical microcanonical flux-flux correlation function. We then give a discussion of the short-time and harmonic limits.

physics.chem-ph↗

arXiv2010

Quantum Theory of Reactive Scattering in Phase Space

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 for determining reactions in high dimensional Hamiltonian systems. This has led to the understanding that a new (to reaction dynamics) type of phase space structure, a {\em normally hyperbolic invariant manifold} (or, NHIM) is the "anchor" on which the phase space structures governing reaction dynamics are built. The quantum normal form theory provides a method for quantizing these phase space structures through the use of the Weyl quantization procedure. We show that this approach provides a solution of the time-independent Schrödinger equation leading to a (local) S-matrix in a neighborhood of the saddle point governing the reaction. It follows easily that the quantization of the directional flux through the dividing surface with the properties noted above is a flux operator that can be expressed in a "closed form". Moreover, from the local S-matrix we easily obtain an expression for the cumulative reactio probability (CRP). Significantly, the expression for the CRP can be evaluated without the need to compute classical trajectories. The quantization of the NHIM is shown to lead to the activated complex, and the lifetimes of quantum states initialized on the NHIM correspond to the Gamov-Siegert resonances. We apply these results to the collinear nitrogen exchange reaction and a three degree-of-freedom system corresponding to an Eckart barrier coupled to two Morse oscillators.

quant-ph↗

arXiv2010

Domain wall motion in ferromagnetic nanowires driven by arbitrary time-dependent fields: An exact result

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 with arbitrary strength and time dependence. We further extend this solution to applied fields slowly varying in space and to multiple domain walls.

cond-mat.mtrl-sci↗

arXiv2010

A periodic orbit formula for quantum reactions through transition states

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 associated Gamov-Siegert resonances. In this letter these results are used to express the cumulative reaction probability as an absolutely convergent sum over periodic orbits contained in the transition state.

nlin.CD↗

arXiv2009

The Quantum Normal Form Approach to Reactive Scattering: The Cumulative Reaction Probability for Collinear Exchange Reactions

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 like the nitrogen exchange reaction the quantum normal form approach gives excellent results and has major computational benefits over full reactive scattering approaches. For light atom systems like the hydrogen exchange reaction however the quantum normal approach is shown to give only poor results. This failure is attributed to the importance of tunnelling trajectories in light atom reactions that are not captured by the quantum normal form as indicated by the only very slow convergence of the quantum normal form for such systems.

physics.chem-ph↗

arXiv2009

Long-time saturation of the Loschmidt echo in quantum chaotic billiards

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. However, until now no quantitative results have been known and, in particular, no explicit expression for the proportionality constant has been proposed. In this paper we perform a quantitative analysis of the phenomenon of the LE saturation and provide the analytical expression for its long-time saturation value for a semiclassical particle in a two-dimensional chaotic billiard. We further perform extensive (fully quantum mechanical) numerical calculations of the LE saturation value and find the numerical results to support the semiclassical theory.

nlin.CD↗

arXiv2008

Loschmidt echo for local perturbations: non-monotonous cross-over from the Fermi-golden-rule to the escape-rate regime

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 identify different decay regimes which complement those known for the case of global perturbations. For weak perturbations a Fermi-golden-rule (FGR) type behavior is recovered. For strong perturbations the escape-rate regime is reached, where the LE decays exponentially with a rate independent of the perturbation strength. The transition between the FGR regime and the escape-rate regime is non-monotonic, i.e. the rate of the exponential time-decay of the LE oscillates as a function of the perturbation strength. We further perform extensive quantum mechanical calculations of the LE based on numerical wave packet evolution which strongly support our semiclassical theory. Finally, we discuss in some detail possible experimental realizations for observing the predicted behavior of the LE.

nlin.CD↗

arXiv2008

Semiclassical Mechanism for the Quantum Decay in Open Chaotic Systems

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) pairs of interfering, correlated classical trajectories are of vital importance. They also provide the dynamical mechanism for related phenomena such as photo-ionization and -dissociation, for which we compute cross section correlations. Moreover, these orbits allow us to establish a semiclassical version of the continuity equation.

cond-mat.mes-hall↗

arXiv2007

Loschmidt echo decay from local boundary perturbations

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 the classical escape rate from an open billiard obtained from the original one by removing the perturbation-affected region of its boundary. Finally, we propose a principal scheme for the experimental observation of the LE decay.

nlin.CD↗

arXiv2006

Wave packet autocorrelation functions for quantum hard-disk and hard-sphere billiards in the high-energy, diffraction regime

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 the wave packet in the high-energy diffraction regime, in which the particle's de Broglie wave length, while being small compared to the size of the scatterers, is large enough to prevent the formation of geometric shadow over distances of the order of the particle's free flight path. The hard-disk or hard-sphere scattering system must be sufficiently dilute in order for this high-energy diffraction regime to be achievable. Apart from the overall exponential decay, the autocorrelation function exhibits a generally complicated sequence of relatively strong peaks corresponding to partial revivals of the wave packet. Both the exponential decay (or escape) rate and the revival peak structure are predominantly determined by the underlying classical dynamics. A relation between the escape rate, and the Lyapunov exponents and Kolmogorov-Sinai entropy of the counterpart classical system, previously known for hard-disk billiards, is strengthened by generalization to three spatial dimensions. The results of the quantum mechanical calculation of the time-dependent autocorrelation function agree with predictions of the semiclassical periodic orbit theory.

nlin.CD↗

arXiv2006

Lyapunov Spreading of Semi-classical Wave Packets for the Lorentz Gas: Theory and Applications

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 semi-classical 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 describe the exponential separation of trajectories in the classical version of this system. This result relates the spread of the wave packet to the rate of separation of classical trajectories, characterized by positive Lyapunov exponents. We consider applications of these results, first to illustrate the behavior of the wave-packet auto-correlation functions for wave packets on periodic orbits. The auto-correlation function can be related to the fidelity, or Loschmidt echo, for the special case that the perturbation is a small change in the mass of the particle. An exact expression for the fidelity, appropriate for this perturbation, leads to an analytical result valid over very long time intervals, inversely proportional to the size of the mass perturbation. For such perturbations, we then calculate the long-time echo for semi-classical wave packets on periodic orbits. This paper also corrects an earlier calculation for a quantum echo, included in a previous version of this paper. We explain the reasons for this correction.

nlin.CD↗