arXiv subjects

Claude Aslangul

Publications and source records attributed to Claude Aslangul.

7 recordsLinked to original sources

arXiv2017

A method for solving gyroscopic equations with operators

The dynamics of a set of identical spins interacting with another one through a time-dependent coupling gives rise to a gyroscopic equation with a variable Larmor frequency and, more importantly, with an operator playing the role a Larmor vector. The subsequent technical complexity is due to non-trivial algebraic relations between multiple inner products coming from the non-commutative algebra of the angular momenta. A general formalism is derived giving the integrated solution valid for all values of the involved spins, and several applications of the formalism are treated in details. Among other results, it is seen that, starting from a fully polarised state for the set of identical spins, their total spin can at most only partially flip (in the mean); this somewhat surprising fact means that the memory of the initial state is kept for ever but varying the coupling constant allows to adjust at will the possible polarisation of the final state. The robustness of the initial state is shown to depend on the nature fermionic or bosonic of the perturbing spin and also on the size of the collection of identical spins.

quant-ph↗

arXiv2007

Surprises in the suddenly-expanded infinite well

I study the time-evolution of a particle prepared in the ground state of an infinite well after the latter is suddenly expanded. It turns out that the probability density $|Ψ(x, t)|^{2}$ shows up quite a surprising behaviour: for definite times, {\it plateaux} appear for which $|Ψ(x, t)|^{2}$ is constant on finite intervals for $x$. Elements of theoretical explanation are given by analyzing the singular component of the second derivative $\partial_{xx}Ψ(x, t)$. Analytical closed expressions are obtained for some specific times, which easily allow to show that, at these times, the density organizes itself into regular patterns provided the size of the box in large enough; more, above some critical time-dependent size, the density patterns are independent of the expansion parameter. It is seen how the density at these times simply results from a construction game with definite rules acting on the pieces of the initial density.

quant-ph↗

arXiv2004

Quantum Dynamics of a Particle with a Spin-dependent Velocity

We study the dynamics of a particle in continuous time and space, the displacement of which is governed by an internal degree of freedom (spin). In one definite limit, the so-called quantum random walk is recovered but, although quite simple, the model possesses a rich variety of dynamics and goes far beyond this problem. Generally speaking, our framework can describe the motion of an electron in a magnetic sea near the Fermi level when linearisation of the dispersion law is possible, coupled to a transverse magnetic field. Quite unexpected behaviours are obtained. In particular, we find that when the initial wave packet is fully localized in space, the $J_{z}$ angular momentum component is frozen; this is an interesting example of an observable which, although it is not a constant of motion, has a constant expectation value. For a non-completely localized wave packet, the effect still occurs although less pronounced, and the spin keeps for ever memory of its initial state. Generally speaking, as time goes on, the spatial density profile looks rather complex, as a consequence of the competition between drift and precession, and displays various shapes according to the ratio between the Larmor period and the characteristic time of flight. The density profile gradually changes from a multimodal quickly moving distribution when the scatttering rate is small, to a unimodal standing but flattening distribution in the opposite cas case.

quant-ph↗

arXiv2000

Effect of a forbidden site on a d-dimensional lattice random walk

We study the effect of a single excluded site on the diffusion of a particle undergoing random walk in a d-dimensional lattice. The determination of the characteristic function allows to find explicitly the asymptotical behaviour of physical quantities such as the particle average position (drift) and the mean square deviation. Contrarily to the one-dimensional case, where the average coordinate diverges at infinite times as t**1/2 and where the diffusion constant D is changed due to the impurity, the effects of the latter are shown to be much less important in higher dimensions: for d=842, the position is simply shifted by a constant and the diffusion constant remains unaltered although dynamical corrections (logarithmic for d=2) still occur. Finally, the continuum space version of the model is analyzed; it is shown that d=1 is the lower dimensionality above which all the effects of the forbidden site are irrelevant.

cond-mat↗

arXiv1999

Single-file Diffusion with Random Diffusion Constants

The single-file problem of N particles in one spatial dimension is analyzed, when each particle has a randomly distributed diffusion constant D sampled in a density $ρ(D)$. The averaged one-particle distributions of the edge particles and the asymptotic ($N\gg 1$) behaviours of their transport coefficients (anomalous velocity and diffusion constant) are strongly dependent on the D-distribution law, broad or narrow. When $ρ$ is exponential, it is shown that the average one-particle front for the edge particles does not shrink when N becomes very large, as contrasted to the pure (non-disordered) case. In addition, when $ρ$ is a broad law, the same occurs for the averaged front, which can even have infinite mean and variance. On the other hand, it is shown that the central particle, dynamically trapped by all others as it is, follows a narrow distribution, which is a Gaussian (with a diffusion constant scaling as $N^{-1}$) when the fractional moment $ $ exists and is finite; otherwise ($ρ(D)\propto D^{α-1}, α\le\case12$), this density is, far from the origin, a stretched exponential with an exponent in the range $]0, 2]$; then the effective diffusion constant scales as $N^{-β}$, with $β= 1/(2α)$.

cond-mat.stat-mech↗

arXiv1999

Diffusion of two repulsive particles in a one-dimensional lattice

The problem of the lattice diffusion of two particles coupled by a contact repulsive interaction is solved by finding analytical expressions of the two-body probability characteristic function. The interaction induces anomalous drift with a vanishing velocity, the average coordinate of each particle growing at large times as $t^{1/2}$. The leading term of the mean square dispersions displays normal diffusion, with a diffusion constant made smaller by the interaction by the non-trivial factor $1-1/π$. Space continuous limit taken from the lattice calculations allows to establish connection with the standard problem of diffusion of a single fictitious particle constrained by a totally reflecting wall. Comparison between lattice and continuous results display marked differences for transient regimes, relevant with regards to high time resolution experiments, and in addition show that, due to slowly decreasing subdominant terms, lattice effects persist even at very large times.

cond-mat↗

arXiv1999

Classical diffusion of N interacting particles in one dimension: General results and asymptotic laws

I consider the coupled one-dimensional diffusion of a cluster of N classical particles with contact repulsion. General expressions are given for the probability distributions, allowing to obtain the transport coefficients. In the limit of large N, and within a gaussian approximation, the diffusion constant is found to behave as N^{-1} for the central particle and as (\ln N)^{-1} for the edge ones. Absolute correlations between the edge particles increase as (\ln N)^{2}. The asymptotic one-body distribution is obtained and discussed in relation of the statistics of extreme events.

cond-mat↗