arXiv subjects

Jan Wehr

Publications and source records attributed to Jan Wehr.

At least 19 recordsLinked to original sources

arXiv2026

Distinguishing synthetic unravelings on quantum computers

Distinct monitoring or intervention schemes can produce different conditioned stochastic quantum trajectories while sharing the same unconditional (ensemble-averaged) dynamics. This is the essence of unravelings of a given Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation: any trajectory-ensemble average of a function that is linear in the conditional state is completely determined by the unconditional density matrix, whereas applying a nonlinear function before averaging can yield unraveling-dependent results beyond the average evolution. A paradigmatic example is resonance fluorescence, where direct photodetection (jump/Poisson) and homodyne or heterodyne detection (diffusive/Wiener) define inequivalent unravelings of the same GKSL dynamics. In earlier work, we showed that nonlinear trajectory averages can distinguish such unravelings, but observing the effect in that optical setting requires demanding experimental precision. Here we translate the same idea to a digital setting by introducing synthetic unravelings implemented as quantum circuits acting on one and two qubits. We design two unravelings - a projective measurement unraveling and a random-unitary "kick" unraveling - that share the same ensemble-averaged evolution while yielding different nonlinear conditional-state statistics. We implement the protocols on superconducting-qubit hardware provided by IBM Quantum to access trajectory-level information. We show that the variance across trajectories and the ensemble-averaged von Neumann entropy distinguish the unravelings in both theory and experiment, while the unconditional state and the ensemble-averaged expectation values that are linear in the state remain identical. Our results provide an accessible demonstration that quantum trajectories encode information about measurement backaction beyond what is fixed by the unconditional dynamics.

quant-ph↗

arXiv2024

Anderson localization induced by structural disorder

We examine the onset of Anderson localization in three-dimensional systems with structural disorder in the form of lattice irregularities and in the absence of any on-site disordered potential. Analyzing two models with distinct types of lattice regularities, we show that the Anderson localization transition occurs when the strength of the structural disorder is smoothly increased. Performing finite-size scaling analysis of the results, we show that the transition belongs to the same universality class as regular Anderson localization induced by onsite disorder. Our work identifies a new class of structurally disordered lattice models in which destructive interference of matter waves may inhibit transport and lead to a transition between metallic and localized phases.

cond-mat.dis-nn↗

arXiv2024

Nonlinear functionals of master equation unravelings

Unravelings provide a probabilistic representation of solutions of master equations and a method of computation of the density operator dynamics. The trajectories generated by unravelings may also be treated as real -- as in the stochastic collapse models. While averages of linear functionals of the unraveling trajectories can be calculated from the master equation, the situation is different for nonlinear functionals, thanks to the corrections with nonzero expected values, coming from the It\^o formula. Two types of nonlinear functionals are considered here: variance, and entropy. The corrections are calculated explicitly for two types of unravelings, based on Poisson and Wiener processes. In the case of entropy, these corrections are shown to be negative, expressing the localization introduced by the Lindblad operators.

quant-ph↗

arXiv2023

Telling different unravelings apart via nonlinear quantum-trajectory averages

The Gorini-Kossakowski-Sudarshan-Lindblad master equation (ME) governs the density matrix of open quantum systems (OQSs). When an OQS is subjected to weak continuous measurement, its state evolves as a stochastic quantum trajectory, whose statistical average solves the ME. The ensemble of such trajectories is termed an unraveling of the ME. We propose a method to operationally distinguish unravelings produced by the same ME in different measurement scenarios, using nonlinear averages of observables over trajectories. We apply the method to the paradigmatic quantum nonlinear system of resonance fluorescence in a two-level atom. We compare the Poisson-type unraveling, induced by direct detection of photons scattered from the two-level emitter, and the Wiener-type unraveling, induced by phase-sensitive detection of the emitted field. We show that a quantum-trajectory-averaged variance is able to distinguish these measurement scenarios. We evaluate the performance of the method, which can be readily extended to more complex OQSs, under a range of realistic experimental conditions.

quant-ph↗

arXiv2023

Equations driven by fast-oscillating functions of an It\^o diffusion process

We study It\^o SDE systems driven by oscillating functions of a single It\^o diffusion process. In the limit when oscillations become fast, we show that the solution process converges in law to the process defined by an SDE system driven by a multivariate Wiener process whose covariance we calculate explicitly. Interestingly, the limiting system of SDEs are most naturally stated using the Stratonovich integral. The problem has been originally motivated by experimental work and special cases of theorems proved here provide a rigorous treatment of equations arising from physics.

math.PR↗

arXiv2022

Haake-Lewenstein-Wilkens approach to spin-glasses revisited

We revisit the Haake-Lewenstein-Wilkens (HLW) approach to Edwards-Anderson (EA) model of Ising spin glass [Phys. Rev. Lett. 55, 2606 (1985)]. This approach consists in evaluation and analysis of the probability distribution of configurations of two replicas of the system, averaged over quenched disorder. This probability distribution generates squares of thermal copies of spin variables from the two copies of the systems, averaged over disorder, that is the terms that enter the standard definition of the original EA order parameter, qEA. We use saddle point/steepest descent method to calculate the average of the Gaussian disorder in higher dimensions. This approximate result suggest that qEA >0 at 0 <T <Tc in 3D and 4D. The case of 2D seems to be a little more subtle, since in the present approach energy increase for a domain wall competes with boundary/edge effects more strongly in 2D; still our approach predicts spin glass order at sufficiently low temperature. We speculate, how these predictions confirm/contradict widely spread opinions that: i) There exist only one (up to the spin flip) ground state in EA model in 2D, 3D and 4D; ii) There is (no) spin glass transition in 3D and 4D (2D). This paper is dedicated to the memories of Fritz Haake and Marek Cieplak.

cond-mat.dis-nn↗

arXiv2020

An averaging approach to the Smoluchowski-Kramers approximation in the presence of a varying magnetic field

We study the small mass limit of the equation describing planar motion of a charged particle of a small mass $\mu$ in a force field, containing a magnetic component, perturbed by a stochastic term. We regularize the problem by adding a small friction of intensity $\e>0$. We show that for all small but fixed frictions the small mass limit of $q_{\mu, \e}$ gives the solution $q_\e$ to a stochastic first order equation, containing a noise-induced drift term. Then, by using a generalization of the classical averaging theorem for Hamiltonian systems by Freidlin and Wentzell, we take the limit of the slow component of the motion $q_\e$ and we prove that it converges weakly to a Markov process on the graph obtained by identifying all points in the same connected components of the level sets of the magnetic field intensity function.

math.PR↗

arXiv2019

Overdamped dynamics of a Brownian particle levitated in a Paul trap

We study the dynamics of the center of mass of a Brownian particle levitated in a Paul trap. We focus on the overdamped regime in the context of levitodynamics, comparing theory with our numerical simulations and experimental data from a nanoparticle in a Paul trap. We provide an exact analytical solution to the stochastic equation of motion, expressions for the standard deviation of the motion, and thermalization times by using the WKB method under two different limits. Finally, we prove the power spectral density of the motion can be approximated by that of an Ornstein-Uhlenbeck process and use the found expression to calibrate the motion of a trapped particle.

cond-mat.stat-mech↗

arXiv2019

Poisson stochastic master equation unravellings and the measurement problem: a quantum stochastic calculus perspective

The paper studies a class of quantum stochastic differential equations, modeling an interaction of a system with its environment in the quantum noise approximation. The space representing quantum noise is the symmetric Fock space over L^2(R_+). Using the isomorphism of this space with the space of square-integrable functionals of the Poisson process, the equations can be represented as classical stochastic differential equations, driven by Poisson processes. This leads to a discontinuous dynamical state reduction which we compare to the Ghirardi-Rimini-Weber model. A purely quantum object, the norm process, is found which plays the role of an observer (in the sense of Everett [H. Everett III, Reviews of modern physics, 29.3, 454, (1957)]), encoding all events occurring in the system space. An algorithm introduced by Dalibard et al [J. Dalibard, Y. Castin, and K. M{\o}lmer, Physical review letters, 68.5, 580 (1992)] to numerically solve quantum master equations is interpreted in the context of unravellings and the trajectories of expected values of system observables are calculated.

math-ph↗

arXiv2019

A small delay and correlation time limit of stochastic differential delay equations with state-dependent colored noise

We consider a general stochastic differential delay equation (SDDE) with state-dependent colored noises and derive its limit as the time delays and the correlation times of the noises go to zero. The work is motivated by an experiment involving an electrical circuit with noisy, delayed feedback. An Ornstein-Uhlenbeck process is used to model the colored noise. The main methods used in the proof are a theorem about convergence of solutions of stochastic differential equations by Kurtz and Protter and a maximal inequality for sums of a stationary sequence of random variables by Peligrad and Utev.

math-ph↗

arXiv2019

Homogenization for Generalized Langevin Equations with Applications to Anomalous Diffusion

We study homogenization for a class of generalized Langevin equations (GLEs) with state-dependent coefficients and exhibiting multiple time scales. In addition to the small mass limit, we focus on homogenization limits, which involve taking to zero the inertial time scale and, possibly, some of the memory time scales and noise correlation time scales. The latter are meaningful limits for a class of GLEs modeling anomalous diffusion. We find that, in general, the limiting stochastic differential equations (SDEs) for the slow degrees of freedom contain non-trivial drift correction terms and are driven by non-Markov noise processes. These results follow from a general homogenization theorem stated and proven here. We illustrate them using stochastic models of particle diffusion.

math-ph↗

arXiv2018

Langevin equations in the small-mass limit: Higher-order approximations

We study the small-mass (overdamped) limit of Langevin equations for a particle in a potential and/or magnetic field with matrix-valued and state-dependent drift and diffusion. We utilize a bootstrapping argument to derive a hierarchy of approximate equations for the position degrees of freedom that are able to achieve accuracy of order $m^{\ell/2}$ over compact time intervals for any $\ell\in\mathbb{Z}^+$. This generalizes prior derivations of the homogenized equation for the position degrees of freedom in the $m\to 0$ limit, which result in order $m^{1/2}$ approximations. Our results cover bounded forces, for which we prove convergence in $L^p$ norms, and unbounded forces, in which case we prove convergence in probability.

math-ph↗

arXiv2018

A homogenization theorem for Langevin systems with an application to Hamiltonian dynamics

This paper studies homogenization of stochastic differential systems. The standard example of this phenomenon is the small mass limit of Hamiltonian systems. We consider this case first from the heuristic point of view, stressing the role of detailed balance and presenting the heuristics based on a multiscale expansion. This is used to propose a physical interpretation of recent results by the authors, as well as to motivate a new theorem proven here. Its main content is a sufficient condition, expressed in terms of solvability of an associated partial differential equation ("the cell problem"), under which the homogenization limit of an SDE is calculated explicitly. The general theorem is applied to a class of systems, satisfying a generalized detailed balance condition with a position-dependent temperature.

math-ph↗

arXiv2018

Small Mass Limit of a Langevin Equation on a Manifold

We study damped geodesic motion of a particle of mass $m$ on a Riemannian manifold, in the presence of an external force and noise. Lifting the resulting stochastic differential equation to the orthogonal frame bundle, we prove that, as $m \to 0$, its solutions converge to solutions of a limiting equation which includes a {\it noise-induced drift} term. A very special case of the main result presents Brownian motion on the manifold as a limit of inertial systems.

math-ph↗

arXiv2018

Phototactic Robot Tunable by Sensorial Delays

The presence of a delay between sensing and reacting to a signal can determine the long-term behavior of autonomous agents whose motion is intrinsically noisy. In a previous work [M. Mijalkov, A. McDaniel, J. Wehr, and G. Volpe, Phys. Rev. X 6, 011008 (2016)], we have shown that sensorial delay can alter the drift and the position probability distribution of an autonomous agent whose speed depends on the illumination intensity it measures. Here, using theory, simulations, and experiments with a phototactic robot, we generalize this effect to an agent for which both speed and rotational diffusion depend on the illumination intensity and are subject to two independent sensorial delays. We show that both the drift and the probability distribution are influenced by the presence of these sensorial delays. In particular, the radial drift may have positive as well as negative sign, and the position probability distribution peaks in different regions depending on the delay. Furthermore, the presence of multiple sensorial delays permits us to explore the role of the interaction between them.

physics.bio-ph↗

arXiv2017

Homogenization of Dissipative, Noisy, Hamiltonian Dynamics

We study the dynamics of a class of Hamiltonian systems with dissipation, coupled to noise, in a singular (small mass) limit. We derive the homogenized equation for the position degrees of freedom in the limit, including the presence of a {\em noise-induced drift} term. We prove convergence to the solution of the homogenized equation in probability and, under stronger assumptions, in an $L^p$-norm. Applications cover the overdamped limit of particle motion in a time-dependent electromagnetic field, on a manifold with time-dependent metric, and the dynamics of nuclear matter.

math-ph↗

arXiv2017

On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion

We study the small mass limit (or: the Smoluchowski-Kramers limit) of a class of quantum Brownian motions with inhomogeneous damping and diffusion. For Ohmic bath spectral density with a Lorentz-Drude cutoff, we derive the Heisenberg-Langevin equations for the particle's observables using a quantum stochastic calculus approach. We set the mass of the particle to equal $m = m_{0} \epsilon$, the reduced Planck constant to equal $\hbar = \epsilon$ and the cutoff frequency to equal $\Lambda = E_{\Lambda}/\epsilon$, where $m_0$ and $E_{\Lambda}$ are positive constants, so that the particle's de Broglie wavelength and the largest energy scale of the bath are fixed as $\epsilon \to 0$. We study the limit as $\epsilon \to 0$ of the rescaled model and derive a limiting equation for the (slow) particle's position variable. We find that the limiting equation contains several drift correction terms, the quantum noise-induced drifts, including terms of purely quantum nature, with no classical counterparts.

cond-mat.stat-mech↗

arXiv2017

Homogenization for a Class of Generalized Langevin Equations with an Application to Thermophoresis

We study a class of systems whose dynamics are described by generalized Langevin equations with state-dependent coefficients. We find that in the limit, in which all the characteristic time scales vanish at the same rate, the position variable of the system converges to a homogenized process, described by an equation containing additional drift terms induced by the noise. The convergence results are obtained using the main result in \cite{hottovy2015smoluchowski}, whose version is proven here under a weaker spectral assumption on the damping matrix. We apply our results to study thermophoresis of a Brownian particle in a non-equilibrium heat bath.

math-ph↗