Sabine Jansen

Mathematical Physics and Statistics

Ludwig-Maximilians-Universität München

Mathematical Institute

Theresienstr. 39

80333 Munich

+49 / 89 2180 4477

jansen[at]math.lmu.de

Research webpage

I love problems that combine physical intuition with mathematical precision and elegance and draw on different styles of reasoning. Eureka moments involve beautiful landscapes of structure emerging after long struggles in understanding, but also being able to pin down subtle nuances in models and reasoning, using mathematical language to bring clarity to interdisciplinary dialogue.

Description

My research within MCQST / MQC focuses on the interplay between probabilistic techniques and analytic tools to understand many-body systems.


Examples of fruitful interplay abound:

  • metastability and the rigorous proof of Arrhenius laws build on the semi-classical limit and WKB expansions;
  • spatial correlations are studied by investigating operators (Stein operators, infinitesimal generators) and their spectral gap, compare the exponential clustering theorem for gapped Hamilton operators;
  • unitary equivalence of Hamilton operators, e.g. based on different representations for algebras of creation and annihilation operators, is closely related to the notion of duality of Markov processes, which might prove helpful in investigating path integrals.


I am especially interested in low-temperature equilibrium states and phase transitions.

Publications

Thermodynamics of a hierarchical mixture of cubes

S. Jansen.

Journal of Statistical Physics (2020).

Show Abstract

We investigate a toy model for phase transitions in mixtures of incompressible droplets. The model consists of non-overlapping hypercubes in Zd of sidelengths 2j, j?N0. Cubes belong to an admissible set B such that if two cubes overlap, then one is contained in the other. Cubes of sidelength 2j have activity zj and density ?j. We prove explicit formulas for the pressure and entropy, prove a van-der-Waals type equation of state, and invert the density-activity relations. In addition we explore phase transitions for parameter-dependent activities zj(?)=exp(2dj??Ej). We prove a sufficient criterion for absence of phase transition, show that constant energies Ej?? lead to a continuous phase transition, and prove a necessary and sufficient condition for the existence of a first-order phase transition.

DOI: 10.1007/s10955-020-02531-1

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