About

Anatoli Polkovnikov is a Professor in the Department of Physics and the Division of Materials Science & Engineering at Boston University. He holds a Ph.D. from Yale University, earned in 2003 under the supervision of Subir Sachdev, and an M.S. from St. Petersburg State Polytechnical University obtained in 1998. His research focuses on understanding various properties of interacting many-particle systems, especially those driven away from equilibrium. His areas of interest include strongly correlated systems, the physics of cold atoms and spin systems, and superconductivity. Professor Polkovnikov's work involves the representation of quantum dynamics through classical trajectories, understanding non-equilibrium thermodynamics from microscopics, exploring universal aspects of dissipation during nearly adiabatic evolution, and studying dynamics near phase transitions. His research is closely tied to experiments in cold atom systems, aiming to deepen the understanding of complex quantum phenomena and their applications.

Research topics

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

Selected publications

• Data for "Temperature and integrability-breaking correspondence via adiabatic transformations" [arXiv:2604.01285]

  Zenodo (CERN European Organization for Nuclear Research) · 2026-03-31

  datasetOpen accessSenior author

  Data and scripts for figures in manuscript titled "Temperature and integrability-breaking correspondence via adiabatic transformations" [arXiv:2604.01285].

  PublisherDOI

• Data for "Temperature and integrability-breaking correspondence via adiabatic transformations" [arXiv:2604.01285]

  Zenodo (CERN European Organization for Nuclear Research) · 2026-03-31

  datasetOpen accessSenior author

  Data and scripts for figures in manuscript titled "Temperature and integrability-breaking correspondence via adiabatic transformations" [arXiv:2604.01285].

  PublisherDOI

• Partial Reversibility and Counterdiabatic Driving in Nearly Integrable Systems

  Open MIND · 2026-02-25

  preprint

  Adiabatic (or reversible) processes are the key concept unifying our understanding of thermodynamics and dynamical systems. Reversibility in the thermodynamic sense is understood as entropy-preserving processes, such as in the idealized Carnot engine, whereas in integrable dynamical systems it is understood as the conservation of the action variables. Between these two idealized limits, however, where the phase space can become mixed, things are much less clear. In this work, we first determine the extent to which reversible processes are even possible in this regime. We then explore how the dissipative losses resulting from rapidly driving these kinds of systems can be fought by approximate counterdiabatic driving. Finally, we argue that much of the phenomenology should be the same for quantum many-body systems with large degeneracy in the presence of integrability breaking perturbations.

  DOI

• The moving Born–Oppenheimer approximation

  Proceedings of the National Academy of Sciences · 2026-02-13 · 2 citations

  articleOpen accessSenior author

  We develop a mixed quantum-classical framework, dubbed the moving Born-Oppenheimer approximation (MBOA), to describe the dynamics of slow degrees of freedom (DOFs) coupled to fast ones. As in the Born-Oppenheimer approximation (BOA), the fast degrees of freedom adiabatically follow a state that depends on the slow ones. Unlike the BOA, this state depends on both the positions and the momenta of the slow DOFs. We study several model systems: a spin-1/2 particle and a spinful molecule moving in a spatially inhomogeneous magnetic field, and a gas of fast particles coupled to a piston. The MBOA reveals rich dynamics for the slow degree of freedom, including reflection, dynamical trapping, and mass renormalization. It also significantly modifies the state of the fast DOFs. For example, the spins in the molecule are entangled and squeezed, while the gas of fast particles develops gradients that are synchronized with the motion of the piston for a long time. The MBOA can be used to describe both classical and quantum systems and has potential applications in quantum chemistry, correlated materials, atomic physics, molecular dynamics, and quantum sensing.

  PublisherOA PDFDOI

• Partial Reversibility and Counterdiabatic Driving in Nearly Integrable Systems

  arXiv (Cornell University) · 2026-02-25

  articleOpen access

  Adiabatic (or reversible) processes are the key concept unifying our understanding of thermodynamics and dynamical systems. Reversibility in the thermodynamic sense is understood as entropy-preserving processes, such as in the idealized Carnot engine, whereas in integrable dynamical systems it is understood as the conservation of the action variables. Between these two idealized limits, however, where the phase space can become mixed, things are much less clear. In this work, we first determine the extent to which reversible processes are even possible in this regime. We then explore how the dissipative losses resulting from rapidly driving these kinds of systems can be fought by approximate counterdiabatic driving. Finally, we argue that much of the phenomenology should be the same for quantum many-body systems with large degeneracy in the presence of integrability breaking perturbations.

  PublisherOA PDF

• Defining classical and quantum chaos through adiabatic transformations

  Journal of Physics A Mathematical and Theoretical · 2026-01-19 · 5 citations

  preprintOpen access

  Abstract We present a unified formalism which identifies chaos in both quantum and classical systems in an equivalent manner by means of adiabatic transformations . The complexity of adiabatic transformations which preserve classical time-averaged trajectories (quantum eigenstates) in response to Hamiltonian deformations serves as a measure of chaos. This complexity is quantified by the (properly regularized) fidelity susceptibility or, more generally, by the geometric tensor. Physically this measure quantifies (i) long time instabilities of physical observables due to small changes in the Hamiltonian of the system and (ii) irregularity of physical observables contained in low frequency noise. Our exposition clearly showcases the common structures underlying quantum and classical chaos and allows us to distinguish integrable, chaotic but non-thermalizing, and ergodic/mixing regimes. We apply the fidelity susceptibility to a model of two coupled spins and demonstrate that it successfully predicts the universal onset of chaos, both for finite spin S and in the classical limit <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mo accent="false" stretchy="false">→</mml:mo> <mml:mi mathvariant="normal">∞</mml:mi> </mml:mrow> </mml:math> . Interestingly, we find that finite S effects are anomalously large close to integrability.

  PublisherOA PDFDOI

• Temperature and integrability-breaking correspondence via adiabatic transformations

  ArXiv.org · 2026-04-01

  articleOpen accessSenior author

  We reveal a correspondence between temperature and integrability-breaking in classical and quantum many-body systems through the lens of geometry and adiabatic transformations. Decreasing the temperature, obtained in a standard way through the derivative of entropy with respect to energy, steers the system towards an integrable point despite strong integrability-breaking interactions. Auto-correlation functions of local observables exhibit slow relaxation dynamics, which violates ergodicity on the approach to this integrable point. Subsequently, the average fidelity susceptibility of stationary states satisfies scaling relations near the integrable point, in close analogy with continuous phase transitions. We further find that the dynamical exponent encompassing relaxation can be different in the quantum and classical models, depending on dimension of the systems. Collectively, our results establish temperature as a tunable control parameter for chaos and puts it on equal footing with integrability-breaking perturbations.

  PublisherOA PDF

• Probing quantum many-body dynamics using subsystem Loschmidt echos

  ArXiv.org · 2025-01-28

  preprintOpen access

  The Loschmidt echo - the probability of a quantum many-body system to return to its initial state following a dynamical evolution - generally contains key information about a quantum system, relevant across various scientific fields including quantum chaos, quantum many-body physics, or high-energy physics. However, it is typically exponentially small in system size, posing an outstanding challenge for experiments. Here, we experimentally investigate the subsystem Loschmidt echo, a quasi-local observable that captures key features of the Loschmidt echo while being readily accessible experimentally. Utilizing quantum gas microscopy, we study its short- and long-time dynamics. In the short-time regime, we observe a dynamical quantum phase transition arising from genuine higher-order correlations. In the long-time regime, the subsystem Loschmidt echo allows us to quantitatively determine the effective dimension and structure of the accessible Hilbert space in the thermodynamic limit. Performing these measurements in the ergodic regime and in the presence of emergent kinetic constraints, we provide direct experimental evidence for ergodicity breaking due to fragmentation of the Hilbert space. Our results establish the subsystem Loschmidt echo as a novel and powerful tool that allows paradigmatic studies of both non-equilibrium dynamics and equilibrium thermodynamics of quantum many-body systems, applicable to a broad range of quantum simulation and computing platforms.

  PublisherOA PDFDOI

• Universal semiclassical dynamics in disordered two-dimensional systems

  Physical review. B./Physical review. B · 2025-03-20

  article

  The dynamics of disordered two-dimensional systems is much less understood than the dynamics of disordered chains, mainly due to the lack of appropriate numerical methods. We demonstrate that a single-trajectory version of the fermionic truncated Wigner approximation (fTWA) gives unexpectedly accurate results for the dynamics of one-dimensional (1D) systems with moderate or strong disorder. Additionally, the computational complexity of calculations carried out within this approximation is small enough to enable studies of two-dimensional (2D) systems larger than standard fTWA. Using this method, we analyze the dynamics of interacting spinless fermions propagating on disordered 1D and 2D lattices. We find for both spatial dimensions that the imbalance exhibits a universal dependence on the rescaled time $t/{\ensuremath{\xi}}_{W}$, where in two dimensions the timescale ${\ensuremath{\xi}}_{W}$ follows a stretched-exponential dependence on disorder strength.

  PublisherDOI

• Random matrix universality in dynamical correlation functions at late times

  SciPost Physics · 2025-08-20 · 3 citations

  articleOpen access

  We study the behaviour of two-time correlation functions at late times for finite system sizes considering observables whose (one-point) average value does not depend on energy. In the long time limit, we show that such correlation functions display a ramp and a plateau determined by the correlations of energy levels, similar to what is already known for the spectral form factor. The plateau value is determined, in absence of degenerate energy levels, by the fluctuations of diagonal matrix elements, which highlights differences between different symmetry classes. We show this behaviour analytically by employing results from Random Matrix Theory and the Eigenstate Thermalisation Hypothesis, and numerically by exact diagonalization in the toy example of a Hamiltonian drawn from a Random Matrix ensemble and in a more realistic example of disordered spin glasses at high temperature. Importantly, correlation functions in the ramp regime do not show self-averaging behaviour, and, at difference with the spectral form factor the time average does not coincide with the ensemble average.

  PublisherOA PDFDOI

Recent grants

• Non-Equilibrium Dynamics in Closed Interacting Quantum Systems

  NSF · $303k · 2012–2015

• Non-Equilibrium Dynamics in Closed Interacting Quantum Systems

  NSF · $349k · 2015–2018

• Non-Equilibrium Dynamics in Closed Interacting Quantum Systems

  NSF · $390k · 2018–2021

• Non-Equilibrium Dynamics in Closed Interacting Quantum Systems

  NSF · $241k · 2009–2012

• Non-Equilibrium Dynamics in Closed Interacting Quantum Systems

  NSF · $389k · 2021–2025

Frequent coauthors

• Dries Sels

  New York University

  59 shared

• Eugene Demler

  43 shared

• Ana María Rey

  University of Colorado Boulder

  27 shared

• Yariv Kafri

  27 shared

• Mikhail D. Lukin

  Harvard University

  25 shared

• Patrick Cheinet

  Laboratoire Aimé Cotton

  25 shared

• Immanuel Bloch

  25 shared

• Simon Fölling

  Ludwig-Maximilians-Universität München

  25 shared

Labs

• Polkovnikov GroupPI

  Quantum many-body physics and quantum simulation

Education

• Ph.D., Physics

  Moscow State University

  1991

• M.S., Physics

  Moscow State University

  1988

• B.S., Physics

  Moscow State University

  1985