arXiv subjects

Lawrence S. Schulman

Publications and source records attributed to Lawrence S. Schulman.

5 recordsLinked to original sources

arXiv2017

Transition matrix from a random walk

Given a random walk a method is presented to produce a matrix of transition probabilities that is consistent with that random walk. The method is a kind of reverse application of the usual ergodicity and is tested by using a transition matrix to produce a path and then using that path to create the estimate. The two matrices and their predictions are then compared. A variety of situations test the method, random matrices, metastable configurations (for which ergodicity often does not apply) and explicit violation of detailed balance.

physics.gen-ph↗

arXiv2014

Is ergodicity a reasonable hypothesis?

In the physics literature "ergodicity" is taken to mean that a system, including a macroscopic one, visits all microscopic states in a relatively short time. We show that this is an impossibility even if that time is billions of years. We also suggest that this feature does not contradict most physical considerations since those considerations deal with correlations of only a few particles.

cond-mat.stat-mech↗

arXiv2006

Passage-time distributions from a spin-boson detector model

The passage-time distribution for a spread-out quantum particle to traverse a specific region is calculated using a detailed quantum model for the detector involved. That model, developed and investigated in earlier works, is based on the detected particle's enhancement of the coupling between a collection of spins (in a metastable state) and their environment. We treat the continuum limit of the model, under the assumption of the Markov property, and calculate the particle state immediately after the first detection. An explicit example with 15 boson modes shows excellent agreement between the discrete model and the continuum limit. Analytical expressions for the passage-time distribution as well as numerical examples are presented. The precision of the measurement scheme is estimated and its optimization discussed. For slow particles, the precision goes like $E^{-3/4}$, which improves previous $E^{-1}$ estimates, obtained with a quantum clock model.

quant-ph↗

arXiv2006

Investigation of a quantum mechanical detector model for moving, spread-out particles

We investigate a fully quantum mechanical spin model for the detection of a moving particle. This model, developed in earlier work, is based on a collection of spins at fixed locations and in a metastable state, with the particle locally enhancing the coupling of the spins to an environment of bosons. Appearance of bosons from particular spins signals the presence of the particle at the spin location, and the first boson indicates its arrival. The original model used discrete boson modes. Here we treat the continuum limit, under the assumption of the Markov property, and calculate the arrival-time distribution for a particle to reach a specific region.

quant-ph↗

arXiv2006

Imaging geometry through dynamics: the observable representation

For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition probabilities (whether between points in $V$ or between variables defined on $V$) and we focus on its ``slow'' eigenvectors, those with eigenvalues closest to that of the stationary eigenvector. These eigenvectors are the ``observables,'' and they can be used to recover geometrical features of $V$.

cond-mat.stat-mech↗