Work Distributions in 1-D Fermions and Bosons with Dual Contact Interactions

Abstract

We extend the well-known static duality \cite{girardeau1960relationship, cheon1999fermion} between 1-D Bosons and 1-D Fermions to the dynamical version. By utilizing this dynamical duality we find the duality of non-equilibrium work distributions between interacting 1-D bosonic (Lieb-Liniger model) and 1-D fermionic (Cheon-Shigehara model) systems with dual contact interactions. As a special case, the work distribution of the Tonks-Girardeau (TG) gas is identical to that of 1-D free fermionic system even though their momentum distributions are significantly different. In the classical limit, the work distributions of Lieb-Liniger models (Cheon-Shigehara models) with arbitrary coupling strength converge to that of the 1-D noninteracting distinguishable particles, although their elemetary excitations (quasi-particles) obey different statistics, e.g. the Bose-Einstein, the Fermi-Dirac and the fractional statistics. We also present numerical results of the work distributions of Lieb-Liniger model with various coupling strengths, which demonstrate the convergence of work distributions in the classical limit.

8 pages, 2 figure, 2 tables

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Cited by in corpus (5)

• Quantum work statistics close to equilibrium
• The Bose-Fermi duality in quantum Otto heat engine with trapped repulsive Bosons
• Work statistics for sudden quenches in interacting quantum many-body systems
• Statistics of work done in degenerate parametric amplification process
• Efficiently simulating the work distribution of multiple identical bosons with boson sampling