Magnetic-Field-Induced Non-Gaussian Fluctuations in Macroscopic Equilibrium Systems

Abstract

We calculate the magnetic-field dependent nonlinear conductance and noise in a two-dimensional macroscopic inhomogeneous system. If the system does not possess a specific symmetry, the magnetic field induces a nonzero third cumulant of the current even at equilibrium. This cumulant is related to the first and second voltage derivatives of the spectral density and average current in the same way as for mesoscopic quantum-coherent systems, but these quantities may be much larger. The system provides a robust test of a non-equilibrium fluctuation relation. PACS numbers: 73.21.Hb, 73.50.Lw It is commonly believed that equilibrium fluctuations in macroscopic systems are Gaussian [1]. If their correlation length l c is much smaller than all the dimensions of the sample L, this is a direct consequence of the central limit theorem, which says that the sum of a large number of random variables will have approximately normal distribution. This is why higher cumulants of current are usually calculated and measured for mesoscopic systems, whose size is smaller than l c . Typically, l c is the inelastic scattering length and if L < l c , the conductor behaves as a single quantum scatterer. In a macroscopic system, higher cumulants are usually much smaller than the second one. However some fluctuations do not exponentially decay with distance and therefore do not have a definite correlation length. For example, fluctuations of charge density in two-dimensional conductors are screened according to a power law. If they are nonlinearly coupled to the current, this may result in a non-Gaussian noise even in an equilibrium macroscopic system. Below we propose a model of such noise. Moreover, the nonzero equilibrium third cumulant of current in it obeys the fluctuation relations recently derived for mesoscopic systems. Recent studies [5][6][7] showed that the fluctuation relations hold even in a magnetic field that breaks the microscopic reversibility. In particular, they link the contribution to the mean current proportional to magnetic field and quadratic in voltage ∆I ∝ V 2 H to a noise contribution proportional to the temperature, magnetic field, and voltage ∆S ∝ T HV , and to the third cumulant of equilibrium current fluctuations C 0 . Consequently, this cumulant is an odd function of the magnetic field. However the relations obtained in 3T [∂∆S/∂V − T ∂2 ∆I/∂V 2 ], whereas Saito and Utsumi [6] obtained a stronger condition C 0 = 2T ∂∆S/∂V = 6T 2 ∂ 2 ∆I/∂V 2 valid for a more restricted class of systems. The weaker condition permits magnetic field asymmetric conductance and noise even if the third cumulant of the equilibrium noise vanishes.The nonlinear contributions to the average current ∆I ∝ V 2 H were calculated for a number of mesoscopic systems. Sanchez and Polianski and one of the authors [8, 9] investigated a quantum Hall bar with an antidot and a chaotic cavity connected to quantum point contacts. Spivak and Zuyzin [10] calculated this contribution for a mesoscopic diffusive system, whereas Andreev and Glazman [11]...

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Factorial cumulants reveal interactions in counting statistics

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“…(14), to a different statistical distribution, with high-order factorial cumulants governed by Eq. (21).…”

Dynamical Scheme for Interferometric Measurements of Full-Counting Statistics

“…Full counting statistics has found widespread use in theories of quantum electronic circuits, for instance in proposals for detecting entanglement [9,10], revealing interactions [11,12], understanding quasi-probabilities [13][14][15][16], or observing Majorana modes [17][18][19][20][21]. Intimate connections to fluctuation relations at the nano-scale [22][23][24][25][26][27][28][29] and to entanglement entropy in fermionic many-body systems [30][31][32][33][34] have also been discovered.Despite these promising applications, experiments remain scarce. Measurements of FCS are demanding as they require accurate detection of rare events in the tails of the distributions.…”