About

Pavel Wiegmann is a professor in the Department of Physics at The University of Chicago, affiliated with the James Franck Institute, Enrico Fermi Institute, Kadanoff Center for Theoretical Physics, and the College. His research encompasses a broad range of areas within physics, including Condensed Matter Physics, Statistical Mechanics, Mathematical Physics, and Nonlinear Physics. In Condensed Matter Physics, he focuses on electronic physics in low dimensions, quantum magnetism, correlated electronic systems, quantum Hall effects, topological aspects of condensed matter, and electronic systems far from equilibrium. His work in Statistical Mechanics involves non-equilibrium statistical mechanics, critical phenomena governed by conformal symmetry, conformal stochastic processes, stochastic geometry, and random matrix theory. In Mathematical Physics, his interests include integrable models of quantum field theory and statistical mechanics, quantum groups and representation theory, anomalies in quantum field theory, conformal field theory, and quantum gravity. His research in Nonlinear Physics addresses driven non-equilibrium systems, turbulence, fractal aspects of pattern formation, interface dynamics, incommensurate systems, integrable aspects of nonlinear physics, and quantum nonlinear phenomena.

Research topics

• Physics
• Quantum mechanics
• Mechanics
• Classical mechanics
• Quantum electrodynamics

Selected publications

• Finite-gap potentials as a semiclassical limit of the thermodynamic Bethe Ansatz

  arXiv (Cornell University) · 2025-12-22

  preprintOpen access

  We show that the semiclassical limit of thermodynamic Bethe Ansatz equations naturally reconstructs the algebro-geometric spectra of finite-gap periodic potentials. This correspondence is illustrated using the traveling-wave (snoidal) solution of the defocusing modified Korteweg--de Vries equation. In this framework, the Bethe-root distribution of the associated quantum field theory yields an Abelian differential of the second kind on the elliptic Riemann surface specified by the spectral endpoints, a structure central to the algebro-geometric theory of solitons. The semiclassical parameter is identified with the large-rank limit of the internal symmetry group ($O(2N)$) of the underlying quantum field theory (the Gross-Neveu model with a chemical potential). Our analysis indicates that the analytic structure of the spectrum is dictated solely by the Dynkin diagram ($D_N$) and its large-rank limit ($D_\infty$), independently of the particular integrable model used to realize it.

  PublisherDOI

• Chern-Simons modification of fluid mechanics

  Physics Letters B · 2025-07-15

  articleOpen access1st authorCorresponding

  We show that the hydrodynamic of the perfect fluid admits a modification that includes a chiral gravitational anomaly (also called mixed gauge-gravity anomaly) alongside the chiral current anomaly. The modification introduces the gravitational Chern-Simons in a manner similar to Jackiw-Pi deformation of gravity [1] and features spinning flows and an analog of axion in fluid mechanics.

  PublisherDOI

• Finite-gap potentials as a semiclassical limit of the thermodynamic Bethe Ansatz

  ArXiv.org · 2025-12-22

  articleOpen access

  We show that the semiclassical limit of thermodynamic Bethe Ansatz equations naturally reconstructs the algebro-geometric spectra of finite-gap periodic potentials. This correspondence is illustrated using the traveling-wave (snoidal) solution of the defocusing modified Korteweg--de Vries equation. In this framework, the Bethe-root distribution of the associated quantum field theory yields an Abelian differential of the second kind on the elliptic Riemann surface specified by the spectral endpoints, a structure central to the algebro-geometric theory of solitons. The semiclassical parameter is identified with the large-rank limit of the internal symmetry group ($O(2N)$) of the underlying quantum field theory (the Gross-Neveu model with a chemical potential). Our analysis indicates that the analytic structure of the spectrum is dictated solely by the Dynkin diagram ($D_N$) and its large-rank limit ($D_\infty$), independently of the particular integrable model used to realize it.

  PublisherOA PDF

• Fluid dynamics as intersection problem

  ArXiv.org · 2025-12-31

  articleOpen accessSenior author

  We formulate the equations of fluid dynamics as an intersection-theoretic problem on an infinite-dimensional symplectic manifold naturally associated with spacetime. This perspective separates the structures determined by the equation of state and the spacetime geometry from the differential-topological data of spacetime. It leads to a geometric derivation of the covariant formulation of hydrodynamics due to Lichnerowicz and Carter, clarifies the role of the canonical velocity and hydrodynamic invariants, including the asymptotic Hopf invariant and the Ertel invariant, and yields a generalized Kelvin circulation theorem. We also explain the relation between the canonical velocity, the four-velocity, and other choices of hydrodynamic frame. In addition, we identify a five-dimensional geometric origin of the formalism underlying covariant hydrodynamics. The formalism extends naturally to fluids with additional degrees of freedom, including multicomponent fluids, charged fluids, and superfluids, and incorporates the chiral anomaly and Onsager quantization. It also suggests a possible bridge between hydrodynamics, Poisson sigma models, and topological field theories. We further argue that the same intersection-theoretic viewpoint applies to self-dual fields, including chiral bosons in 1+1 dimensions, tensor fields of the (2,0) theory in 1+5 dimensions, and the self-dual four-form field of type-IIB supergravity in 1+9 dimensions.

  PublisherOA PDF

• Fluid dynamics as intersection problem

  arXiv (Cornell University) · 2025-12-31

  preprintOpen accessSenior author

  We formulate the equations of fluid dynamics as an intersection-theoretic problem on an infinite-dimensional symplectic manifold naturally associated with spacetime. This perspective separates the structures determined by the equation of state and the spacetime geometry from the differential-topological data of spacetime. It leads to a geometric derivation of the covariant formulation of hydrodynamics due to Lichnerowicz and Carter, clarifies the role of the canonical velocity and hydrodynamic invariants, including the asymptotic Hopf invariant and the Ertel invariant, and yields a generalized Kelvin circulation theorem. We also explain the relation between the canonical velocity, the four-velocity, and other choices of hydrodynamic frame. In addition, we identify a five-dimensional geometric origin of the formalism underlying covariant hydrodynamics. The formalism extends naturally to fluids with additional degrees of freedom, including multicomponent fluids, charged fluids, and superfluids, and incorporates the chiral anomaly and Onsager quantization. It also suggests a possible bridge between hydrodynamics, Poisson sigma models, and topological field theories. We further argue that the same intersection-theoretic viewpoint applies to self-dual fields, including chiral bosons in 1+1 dimensions, tensor fields of the (2,0) theory in 1+5 dimensions, and the self-dual four-form field of type-IIB supergravity in 1+9 dimensions.

  PublisherDOI

• Multivalued Wess-Zumino-Novikov functional and chiral anomaly in hydrodynamics

  Physical review. D/Physical review. D. · 2024-12-30 · 2 citations

  articleOpen access1st authorCorresponding

  We present a hydrodynamic framework derived from the action of a perfect fluid, modified by the hydrodynamic analog of Novikov’s multivalued functional. This modification introduces spin degrees of freedom into the fluid. The structure closely resembles the Abelian version of the Wess-Zumino functional, commonly applied in field theories with chiral anomalies. The deformation incorporates transport properties of Weyl fermions and, in the case of a charged fluid, exhibits the chiral anomaly. It is also consistent with Onsager’s semiclassical quantization of circulation. Additionally, we discuss the hydrodynamic analog of instantons and related topological invariants. Published by the American Physical Society 2024

  PublisherDOI

• Peierls Transition in Gross-Neveu Model from Bethe Ansatz

  Physical Review Letters · 2024-09-03 · 2 citations

  articleOpen access

  The two-dimensional Gross-Neveu model is anticipated to undergo a crystalline phase transition at high baryon charge densities. This conclusion is drawn from the mean-field approximation, which closely resembles models of Peierls instability. We demonstrate that this transition indeed occurs when both the rank of the symmetry group and the dimension of the particle representation contributing to the baryon density are large (the large N limit). We derive this result through the exact solution of the model, developing the large N limit of the Bethe ansatz. Our analytical construction of the large-N solution of the Bethe ansatz equations aligns perfectly with the periodic (finite-gap) solution of the Korteweg-de Vries (KdV) of the mean-field analysis.

  PublisherDOI

• Fingering patterns in Hele-Shaw flows are density shock wave solutions of dispersionless KdV hierarchy

  OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2024-02-02

  articleOpen accessSenior author

  We investigate the hydrodynamics of a Hele-Shaw flow as the free boundary evolves from smooth initial conditions into a generic cusp singularity (of local geometry type x{sup 3} {approx} y{sup 2}), and then into a density shock wave. This novel solution preserves the integrability of the dynamics and, unlike all the weak solutions proposed previously, is not underdetermined. The evolution of the shock is such that the net vorticity remains zero, as before the critical time, and the shock can be interpreted as a singular line distribution of fluid deficit.

  PublisherOA PDF

• Multivalued Wess-Zumino-Novikov Functional and Chiral Anomaly in Hydrodynamics

  arXiv (Cornell University) · 2024-03-29

  preprintOpen access1st authorCorresponding

  We present a hydrodynamic framework derived from the action of a perfect fluid, modified by the hydrodynamic analog of Novikov's multivalued functional. This modification introduces spin degrees of freedom into the fluid. The structure closely resembles the Abelian version of the Wess-Zumino functional, commonly applied in field theories with chiral anomalies. The deformation incorporates the transport properties of Weyl fermions and exhibits the chiral anomaly in the case of a charged fluid. It is also consistent with Onsager's semiclassical quantization of circulation. Additionally, we discuss the hydrodynamic analog of instantons and related topological invariants.

  PublisherOA PDFDOI

• Peierls Transition in Gross-Neveu Model from Bethe Ansatz

  arXiv (Cornell University) · 2024-04-10

  preprintOpen access

  The two-dimensional Gross-Neveu model is anticipated to undergo a crystalline phase transition at high baryon charge densities. This conclusion is drawn from the mean-field approximation, which closely resembles models of Peierls instability. We demonstrate that this transition indeed occurs when both the rank of the symmetry group and the dimension of the particle representation contributing to the baryon density are large (the large-N limit). We derive this result through the exact solution of the model, developing the large-N limit of the Bethe Ansatz. Our analytical construction of the large-N solution of the Bethe Ansatz equations aligns perfectly with the periodic (finite-gap) solution of the Korteweg-de Vries (KdV) of the mean-field analysis.

  PublisherOA PDFDOI

Recent grants

• Conformal Stochastic Geometry, Dyson Gas, Potential Theory and Conformal Field Theory

  NSF · $150k · 2011–2015

• Theoretical Studies of Quantum Systems with Strong Interactions

  NSF · $400k · 2012–2017

• Theoretical Studies of Quantum Systems with Strong Interaction: Geometry and Topology of Quantum States and Flows

  NSF · $330k · 2020–2025

• Theoretical Studies of Quantum Systems with Strong Interactions

  NSF · $270k · 2006–2010

• Theoretical Studies of Quantum Systems with Strong Interations

  NSF · $300k · 2009–2013

Frequent coauthors

• A. Zabrodin

  61 shared

• Alexander G. Abanov

  38 shared

• Eldad Bettelheim

  Hebrew University of Jerusalem

  21 shared

• I. M. Krichever

  Columbia University

  20 shared

• Tankut Can

  Institute for Advanced Study

  16 shared

• Razvan Teodorescu

  14 shared

• D. V. Khveshchenko

  12 shared

• A.M. Tsvelick

  Landau Institute for Theoretical Physics

  10 shared