arXiv subjects

Alexander Stotland

Publications and source records attributed to Alexander Stotland.

8 recordsLinked to original sources

arXiv2012

Stochastic memory: memory enhancement due to noise

There are certain classes of resistors, capacitors and inductors that, when subject to a periodic input of appropriate frequency, develop hysteresis loops in their characteristic response. Here, we show that the hysteresis of such memory elements can also be induced by white noise of appropriate intensity even at very low frequencies of the external driving field. We illustrate this phenomenon using a physical model of memory resistor realized by $\mathrm{TiO_2}$ thin films sandwiched between metallic electrodes, and discuss under which conditions this effect can be observed experimentally. We also discuss its implications on existing memory systems described in the literature and the role of colored noise.

cond-mat.mes-hall↗

arXiv2011

"Weak Quantum Chaos" and its resistor network modeling

Weakly chaotic or weakly interacting systems have a wide regime where the common random matrix theory modeling does not apply. As an example we consider cold atoms in a nearly integrable optical billiard with displaceable wall ("piston"). The motion is completely chaotic but with small Lyapunov exponent. The Hamiltonian matrix does not look like one taken from a Gaussian ensemble, but rather it is very sparse and textured. This can be characterized by parameters $s$ and $g$ that reflect the percentage of large elements, and their connectivity, respectively. For $g$ we use a resistor network calculation that has a direct relation to the semi-linear response characteristics of the system, hence leading to a novel prediction regarding the rate of heating of cold atoms in optical billiards with vibrating walls.

quant-ph↗

arXiv2010

Quantum response of weakly chaotic systems

Chaotic systems, that have a small Lyapunov exponent, do not obey the common random matrix theory predictions within a wide "weak quantum chaos" regime. This leads to a novel prediction for the rate of heating for cold atoms in optical billiards with vibrating walls. The Hamiltonian matrix of the driven system does not look like one from a Gaussian ensemble, but rather it is very sparse. This sparsity can be characterized by parameters $s$ and $g$ that reflect the percentage of large elements, and their connectivity respectively. For $g$ we use a resistor network calculation that has direct relation to the semi-linear response characteristics of the system.

quant-ph↗

arXiv2010

Random-matrix modeling of semi-linear response, the generalized variable range hopping picture, and the conductance of mesoscopic rings

Semi-linear response theory determines the absorption coefficient of a driven system using a resistor network calculation: Each unperturbed energy level of a particle in a vibrating trap, or of an electron in a mesoscopic ring, is regarded as a node ($n$) of the network; The transition rates ($w_{mn}$) between the nodes are regarded as the elements of a random matrix that describes the network. If the size-distribution of the connecting elements is wide (e.g. log-normal-like rather than Gaussian-like) the result for the absorption coefficient differs enormously from the conventional Kubo prediction of linear response theory. We use a generalized variable range hopping scheme for the analysis. In particular we apply this approach to obtain practical approximations for the conductance of mesoscopic rings. In this context Mott's picture of diffusion and localization is revisited.

cond-mat.mes-hall↗

arXiv2009

Semilinear response for the heating rate of cold atoms in vibrating traps

The calculation of the heating rate of cold atoms in vibrating traps requires a theory that goes beyond the Kubo linear response formulation. If a strong "quantum chaos" assumption does not hold, the analysis of transitions shows similarities with a percolation problem in energy space. We show how the texture and the sparsity of the perturbation matrix, as determined by the geometry of the system, dictate the result. An improved sparse random matrix model is introduced: it captures the essential ingredients of the problem, and leads to a generalized variable range hopping picture.

quant-ph↗

arXiv2008

The mesoscopic conductance of disordered rings, its random matrix theory, and the generalized variable range hopping picture

The calculation of the conductance of disordered rings requires a theory that goes beyond the Kubo-Drude formulation. Assuming "mesoscopic" circumstances the analysis of the electro-driven transitions show similarities with a percolation problem in energy space. We argue that the texture and the sparsity of the perturbation matrix dictate the value of the conductance, and study its dependence on the disorder strength, ranging from the ballistic to the Anderson localization regime. An improved sparse random matrix model is introduced to captures the essential ingredients of the problem, and leads to a generalized variable range hopping picture.

cond-mat.mes-hall↗

arXiv2006

Diffractive energy spreading and its semiclassical limit

We consider driven systems where the driving induces jumps in energy space: (1) particles pulsed by a step potential; (2) particles in a box with a moving wall; (3) particles in a ring driven by an electro-motive-force. In all these cases the route towards quantum-classical correspondence is highly non-trivial. Some insight is gained by observing that the dynamics in energy space, where $n$ is the level index, is essentially the same as that of Bloch electrons in a tight binding model, where $n$ is the site index. The mean level spacing is like a constant electric field and the driving induces long range hopping 1/(n-m).

cond-mat.mes-hall↗

arXiv2004

The information entropy of quantum mechanical states

It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the latter is problematic from quantum information point of view. Consequently we introduce a new definition of entropy that reflects the inherent uncertainty of quantum mechanical states. We derive for it an explicit expression, and discuss some of its general properties. We distinguish between the minimum uncertainty entropy of pure states, and the excess statistical entropy of mixtures.

quant-ph↗