About

Jan Wehr is a Professor of Mathematics and a member of the Graduate Faculty at the University of Arizona. He is affiliated with the Department of Mathematics and specializes in applied mathematics. His contact information includes an email at wehr@arizona.edu and a phone number at 520-621-2834. His office is located at MATH-720, 617 N. Santa Rita Ave., Tucson, AZ 85721-0089. The department offers a variety of academic programs, including undergraduate and graduate degrees in mathematics and statistics, as well as research centers and outreach initiatives. The university emphasizes its commitment to Indigenous communities and building sustainable relationships with Native Nations. Specific details about Professor Wehr's research focus, background, or key contributions are not provided on the page.

Research topics

• Mathematics
• Physics
• Statistical physics
• Mathematical analysis
• Classical mechanics

Selected publications

• Distinguishing synthetic unravelings on quantum computers

  ArXiv.org · 2026-01-27

  articleOpen access

  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.

  PublisherOA PDF

• Distinguishing synthetic unravelings on quantum computers

  Open MIND · 2026-01-27

  preprint

  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.

  DOI

• Anderson localization induced by structural disorder

  Physical review. B./Physical review. B · 2025-05-14 · 2 citations

  articleOpen access

  We examine the onset of Anderson localization in three-dimensional systems with structural disorder in 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, we show that the transition belongs to the same universality class as regular Anderson localization induced by on-site disorder. Our paper identifies a 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.

  PublisherOA PDFDOI

• Nonlinear functionals of master equation unravelings

  arXiv (Cornell University) · 2024-02-08

  preprintOpen accessSenior author

  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 Itô 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.

  PublisherOA PDFDOI

• Telling different unravelings apart via nonlinear quantum-trajectory averages

  Physical Review Research · 2024-09-06 · 2 citations

  articleOpen access

  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. Published by the American Physical Society 2024

  PublisherDOI

• Anderson localization induced by structural disorder

  arXiv (Cornell University) · 2024-11-15

  preprintOpen access

  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.

  PublisherOA PDFDOI

• Spectrum broadcast structures from von Neumann type interaction Hamiltonians

  Journal of Mathematical Physics · 2024-12-01 · 1 citations

  article

  In this paper, we contribute to the mathematical foundations of the recently established theory of Spectrum Broadcast Structures (SBS). These are multipartite quantum states, encoding an operational notion of objectivity and exhibiting a more advanced form of decoherence. We study SBS in the case of a central system interacting with N environments via the von Neumann-type measurement interactions, ubiquitous in the theory of open quantum systems. We state and prove a novel sufficient condition for SBS to arise dynamically for finite-dimensional systems. The condition is based on the Gram–Schmidt orthogonalization rather than on the Knill–Barnum error estimation used in previous papers.

  PublisherDOI

• Telling different unravelings apart via nonlinear quantum-trajectory averages

  arXiv (Cornell University) · 2023-12-06

  preprintOpen access

  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.

  PublisherOA PDFDOI

• Equations driven by fast-oscillating functions of an Itô diffusion process

  arXiv (Cornell University) · 2023-12-04

  preprintOpen accessSenior author

  We study Itô SDE systems driven by oscillating functions of a single Itô 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.

  PublisherOA PDFDOI

• Haake–Lewenstein–Wilkens approach to spin-glasses revisited

  Journal of Physics A Mathematical and Theoretical · 2022-10-24 · 1 citations

  articleSenior author

  Abstract We revisit the Haake–Lewenstein–Wilkens approach to Edwards–Anderson (EA) model of Ising spin glass (SG) (Haake et al 1985 Phys. Rev. Lett. 55 2606). 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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>q</mml:mi> <mml:mrow> <mml:mtext>EA</mml:mtext> </mml:mrow> </mml:msub> </mml:math> . We use saddle point/steepest descent (SPSD) method to calculate the average of the Gaussian disorder in higher dimensions. This approximate result suggest that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>q</mml:mi> <mml:mrow> <mml:mtext>EA</mml:mtext> </mml:mrow> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:math> at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0</mml:mn> <mml:mo>&lt;</mml:mo> <mml:mi>T</mml:mi> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> 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 SG 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) SG transition in 3D and 4D (2D). This paper is dedicated to the memories of Fritz Haake and Marek Cieplak.

  PublisherDOI

Recent grants

• Mathematics of Noisy and Disordered Systems

  NSF · $250k · 2013–2016

• Randomness in Physical Systems

  NSF · $211k · 2010–2013

• Mathematical Physics of Open Systems

  NSF · $370k · 2019–2023

• Mathematics of Noise and Disorder in Classical and Quantum Systems

  NSF · $385k · 2016–2020

• Disordered Atomic Lattice Gases and Quantum Information

  NSF · $100k · 2007–2008

Frequent coauthors

• Maciej Lewenstein

  Institute of Photonic Sciences

  54 shared

• Giovanni Volpe

  23 shared

• Jeremiah Birrell

  16 shared

• J. K. Korbicz

  16 shared

• Krzysztof Sacha

  14 shared

• Armand Niederberger

  Vir Biotechnology (Switzerland)

  12 shared

• Austin McDaniel

  9 shared

• Clemens Bechinger

  University of Konstanz

  8 shared

Education

• Ph.D., Mathematics

  Rutgers University

  1989