arXiv subjects

S. V. Mousavi

Publications and source records attributed to S. V. Mousavi.

At least 37 records · Page 2Linked to original sources

arXiv2019

Stochastic Bohmian mechanics within the Schrödinger-Langevin framework: A trajectory analysis of wave-packet dynamics in a fluctuative-dissipative medium

A Bohmian analysis of the so-called Schrödinger-Langevin or Kostin nonlinear differential equation is provided to study how thermal fluctuations of the environment affects the dynamics of the wave packet from a quantum hydrodynamical point of view. In this way, after obtaining the Schrödinger-Langevin-Bohm equation from the Kostin equation its application to simple but physically insightful systems such as the Brownian-Bohmian motion, motion in a gravity field and transmission through a parabolic repeller is studied. % If a time-dependent Gaussian ansatz for the probability density is assumed, the effect of thermal fluctuations together with thermal wave packets leads to Bohmian stochastic trajectories. From this trajectory based analysis, quantum and classical diffusion coefficients for free particles, thermal arrival times for a linear potential and transmission probabilities and characteristic times such as arrival and dwell times for a parabolic repeller are then presented and discussed.

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arXiv2018

Nonlocality and local causality in the Schrödinger Equation with time-dependent boundary conditions

We investigate the nonlocal dynamics of a single particle placed in an infinite well with moving walls. It is shown that in this situation, the Schrödinger equation (SE) violates local causality by causing instantaneous changes in the probability current everywhere inside the well. This violation is formalized by designing a gedanken faster-than-light communication device which uses an ensemble of long narrow cavities and weak measurements to resolve the weak value of the momentum far away from the movable wall. Our system is free from the usual features causing nonphysical violations of local causality when using the (nonrelativistic) SE, such as instantaneous changes in potentials or states involving arbitrarily high energies or velocities. We explore in detail several possible artifacts that could account for the failure of the SE to respect local causality for systems involving time-dependent boundary conditions.

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arXiv2018

Characteristic times for thermal wave packets in dissipative Bohmian mechanics: the parabolic repeller

Thermal wave packets are used to analyze transmission probabilities and characteristic times through a parabolic repeller within the dissipative Bohmian mechanics. Thermal arrival, dwelling, transmission and reflection times are defined and calculated by using a Maxwell-Boltzmann distribution for the initial velocities of the incident particles. The dissipation is considered within the Caldirola-Kanai and Kostin approaches where a linear and nonlinear framework is used, respectively. The initial parameters are chosen to have only a dissipative tunnelling dynamics at zero temperature; at any nonzero temperature, transmission proceeds not only via tunnelling.

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arXiv2018

Dissipative tunneling by means of scaled trajectories

Dissipative quantum tunnelling through an inverted parabolic barrier is considered in the presence of an electric field. A Schrödinger-Langevin or Kostin quantum classical transition wave equation is used and applied resulting in a scaled differential equation of motion. A Gaussian wave packet solution to the resulting scaled Kostin nonlinear equation is assumed and compared to the same solution for the scaled linear Caldirola-Kanai equation. The resulting scaled trajectories are obtained at different dynamical regimes and friction cases, showing the gradual decoherence process in this open dynamics. Theoretical results show that the transmission probabilities are always higher in the Kostin approach than in the Caldirola-Kanai approach in the presence or not of an external electric field. This discrepancy should be understood due to the presence of an environment since the corresponding open dynamics should be governed by nonlinear quantum equations, whereas the second approach is issued from an effective Hamiltonian within a linear theory.

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arXiv2018

Quantum-classical transition in dissipative systems through scaled trajectories

A nonlinear quantum-classical transition wave equation is proposed for dissipative systems within the Caldirola-Kanai model. Equivalence of this transition equation to a scaled Schrödinger equation is proved. The dissipative dynamics is then studied in terms of what we call scaled trajectories following the standard procedure used in Bohmian mechanics. These trajectories depend on a continuous parameter allowing us a smooth transition from Bohmian to classical trajectories. Arrival times and actual momentum distribution functions are also analyzed. The propagation of a Gaussian wave packet in a viscid medium under the presence of constant, linear and harmonic potentials is studied. The gradual decoherence process and localization are easily visualized and understood within this theoretical framework.

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arXiv2017

Strong and weak single particle nonlocality induced by time-dependent boundary conditions

We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We first prove that contrary to earlier claims, there is no strong nonlocality: a quantum state localized at the center of a well with infinitely high moving walls is not modified by the wall's motion. We then show the existence of a weak form of nonlocality: when a quantum state is extended over the well, the wall's motion induces a current density all over the box instantaneously. We indicate how this current density can in principle be measured by performing weak measurements of the particle's momentum.

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arXiv2015

Effect of quantum statistics on the gravitational weak equivalence principle

We study the effect of quantum statistics on the arrival time distribution of quantum particles computed through the probability current density. It is shown that symmetrization or asymmetrization of the wave function affects the arrival time distribution for even freely propagating particles. In order to investigate the effect of statistics on the weak equivalence principle in quantum mechanics (WEQ), we then compute the mean arrival time for wave packets in free fall. The violation of WEQ through the effect of statistics on the mass-dependence of the mean arrival time is clearly exhibited. We finally evaluate the effect of spin on the violation of WEQ using a different approach by including an explicit spin-dependence in the probability current distribution, and compare it with the approach using particle statistics. Our results show WEQ re-emerges smoothly in the limit of large mass.

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arXiv2015

Scattering by a reflectionless modified Pöschl-Teller potential: Bohmian trajectories and arrival times

A nonreflecting wavepacket is constructed by the superposition of reflectionless eigenstates of sech2 potential. Free propagation and propagation in the presence of the above potential of such a wavepacket is considered using the concept of arrival time. Comparison is made with the free evolving Gaussian wavepacket. Mean arrival time at a detector behind the well is given as a function of mass for separate cases. A selection of Bohmian trajectories in the interacting case are computed and compared to the trajectories of a free particle guided by a Gaussian packet.

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arXiv2015

Quantum-classical comparison: arrival times and statistics

Classical and quantum scattering of a non-Gaussian wave packet by a rectangular barrier is studied in terms of arrival times to a given detector location. A classical wave equation, proposed by N. Rosen [{\it{Am. J. Phys.}} {\bf 32} (1964) 377], is used to study the corresponding classical dynamics. Mean arrival times are then computed and compared for different values of initial wave packet parameters and barrier width. The agreement is improved in the large mass limit as one expects. A short comment on the possibility of generalization of Rosen's proposal to a two-body system is given. Differences in distributions of particles obeying different statistics are studied by considering a system composed of two free particles.

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arXiv2014

Time-dependent potential barriers and superarrivals

Scattering of a Gaussian wavepacket from rectangular potential barriers with increasing widths or heights is studied numerically. It is seen that during a certain time interval the time-evolving transmission probability increases compared to the corresponding unperturbed cases. In the literature this effect is known as superarrival in transmission probability. We present a trajectory-based explanation for this effect by using the concept of quantum potential energy and computing a selection of Bohmian trajectories. Relevant parameters in superarrivals are determined for the case that the barrier width increases linearly during the dispersion of the wavepacket. Nonlinear in time perturbation is also considered.

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arXiv2014

Quantum effective force and Bohmian approach for time-dependent traps

Trajectories of a Bohmian particle confined in time-dependent cylindrical and spherical traps are computed for both contracting and expanding boxes. Quantum effective force is considered in arbitrary directions. It is seen that in contrast to the problem of a particle in an infinite rectangular box with one wall in motion, if particle initially is in an energy eigenstate of a tiny box the force is zero in all directions. Trajectories of a two-body system confined in the spherical trap are also computed for different statistics. Computations show that there are situations for which distance between bosons is greater than the fermions. However, results of average separation of the particles confirm our expectation about the statistics.

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arXiv2013

Quantum dynamics in a time-dependent cylindrical trap

Solutions to the Schrödinger equation are examined for a particle inside a cylindrical trap of a circular time-dependent cross-section. Analytical expressions for energy and momentum expectation values are derived with respect to the exact solutions; and the adiabatic and sudden change of the boundary are discussed. The density profile as a function of time in a given observation point, resembles the diffraction-in-time pattern observed in a suddenly released particle but with an enhanced fringe visibility. Numerical computations are presented for both contracting and expanding boxes.

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arXiv2012

Quantum effective force in an expanding infinite square-well potential and Bohmian perspective

The Schrödinger equation is solved for the case of a particle confined to a small region of a box with infinite walls. If walls of the well are moved, then, due to an effective quantum nonlocal interaction with the boundary, even though the particle is nowhere near the walls, it will be affected. It is shown that this force apart from a minus sign is equal to the expectation value of the gradient of the quantum potential for vanishing at the walls boundary condition. Variation of this force with time is studied. A selection of Bohmian trajectories of the confined particle is also computed.

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arXiv2012

Quantum Dynamics in a Time-dependent Hard-Wall Spherical Trap

Exact solution of the Schrödinger equation is given for a particle inside a hard sphere whose wall is moving with a constant velocity. Numerical computations are presented for both contracting and expanding spheres. The propagator is constructed and compared with the propagator of a particle in an infinite square well with one wall in uniform motion.

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arXiv2011

Strong quantum violation of the gravitational weak equivalence principle by a non-Gaussian wave-packet

The weak equivalence principle of gravity is examined at the quantum level in two ways. First, the position detection probabilities of particles described by a non-Gaussian wave-packet projected upwards against gravity around the classical turning point and also around the point of initial projection are calculated. These probabilities exhibit mass-dependence at both these points, thereby reflecting the quantum violation of the weak equivalence principle. Secondly, the mean arrival time of freely falling particles is calculated using the quantum probability current, which also turns out to be mass dependent. Such a mass-dependence is shown to be enhanced by increasing the non-Gaussianity parameter of the wave packet, thus signifying a stronger violation of the weak equivalence principle through a greater departure from Gaussianity of the initial wave packet. The mass-dependence of both the position detection probabilities and the mean arrival time vanish in the limit of large mass. Thus, compatibility between the weak equivalence principle and quantum mechanics is recovered in the macroscopic limit of the latter. A selection of Bohm trajectories is exhibited to illustrate these features in the free fall case.

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arXiv2011

Diffraction in time of a confined particle and its Bohmian paths

Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schrödinger equation is discussed analytically and numerically for various initial wavefunctions. In each case Bohmian trajectories of the particles are computed and also the mean arrival time at a given location is studied as a function of the initial state.

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arXiv2011

Quantum-mechanical effects in a linear time-dependent potential

The solution of the time-dependent Schrödinger equation is discussed for a particle confined in half-space $x>0$ with a linear potential $V(x)=Kx$ in the following situations: (a) sudden removal of the wall and switching on the linear potential $V(x)=Kx$ at $x \leq 0$, (b) sudden removal of the wall and the potential and (c) sudden removal of the potential. A brief discussion of the quantum statistic is presented.

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arXiv2008

Quantum motion effects in an ultracold-atom Mach-Zehnder interferometer

We study the effect of quantum motion in a Mach-Zehnder interferometer where ultracold, two-level atoms cross a $π/2 $-$π$-$π/2$ configuration of separated, laser illuminated regions. Explicit and exact expressions are obtained for transmission amplitudes of monochromatic, incident atomic waves using recurrence relations which take into account all possible paths: the direct ones usually considered in the simple semiclassical treatment, but including quantum motion corrections, and the paths in which the atoms are repeatedly reflected at the fields.

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