Multifractality of random eigenfunctions and generalization of Jarzynski equality

Abstract

Systems driven out of equilibrium experience large fluctuations of the dissipated work. The same is true for wave function amplitudes in disordered systems close to the Anderson localization transition.\cite{Mirlin-review} In both cases the probability distribution function (PDF) is given by the large deviation ansatz. Here we exploit the analogy between the PDF of work dissipated in a driven single-electron box (SEB) and that of random multifractal wave function amplitudes and uncover new relations which generalize the Jarzynski equality. We checked the new relations experimentally by measuring the dissipated work in a driven SEB and found a remarkable correspondence. The results represent an important universal feature of the work statistics in systems out of equilibrium and help to understand the nature of the symmetry of multifractal exponents in the theory of Anderson localization.

arXiv comment5 pages of the main text, 4 pages of the supplementary materials, 4 figures

References in corpus (28)

• A nonequilibrium equality for free energy differences
• Nonequilibrium dynamics of closed interacting quantum systems
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Anderson Transitions
• The large deviation approach to statistical mechanics
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Experimental realization of a Szilard engine with a single electron
• Thermodynamics of a Colloidal Particle in a Time-Dependent Non-Harmonic Potential
• Experimental study of mutual information in a Maxwell Demon
• Anderson localization on the Bethe lattice: non-ergodicity of extended states
• Test of Jarzynski and Crooks fluctuation relations in an electronic system
• New Class of Random Matrix Ensembles with Multifractal Eigenvectors
• Exact relations between multifractal exponents at the Anderson transition
• Density of states in a superconductor carrying a supercurrent
• Distribution of Entropy Production in a Single-Electron Box
• Bidirectional Single-Electron Counting and the Fluctuation Theorem
• Irreversibility on the Level of Single-Electron Tunneling
• Two-eigenfunction correlation in a multifractal metal and insulator
• Electronic Refrigeration at the Quantum Limit
• Non-adiabadic charge pumping in a hybrid SET transistor
• Statistics of Impedance, Local Density of States, and Reflection in Quantum Chaotic Systems with Absorption
• Recovery of free energy branches in single molecule experiments
• Statistics of the dissipated energy in driven single-electron transitions
• Bound particle coupled to two thermostats
• Modulated two-level system : Exact work statistics
• Symmetry relation for multifractal spectra at random critical points
• Work, free energy and dissipation in voltage driven single-electron transitions
• Critical level statistics and anomalously localized states at the Anderson transition

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• Thermodynamics in Single-Electron Circuits and Superconducting Qubits
• Extreme reductions of entropy in an electronic double dot
• Anatomy of the eigenstates distribution: a quest for a genuine multifractality
• Statistics of a simple transmission mode on a lossy chaotic background
• The distribution of work performed on a NIS junction
• Time-reversal symmetric Crooks and Gallavotti-Cohen fluctuation relations in driven classical Markovian systems
• Conductance of a SET with a retarded dielectric layer in the gate capacitor