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Register a new userFluctuation theorems without time-reversal symmetry
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Fluctuation theorems establish deep relations between observables away from thermal equilibrium. Until recently, the research on fluctuation theorems was focused on time-reversal-invariant systems. In this review we address some newly discovered fluctuation relations that hold without time-reversal symmetry, in particular, in the presence of an external magnetic field. One family of relations connects non-linear transport coefficients in the opposite magnetic fields. Another family relates currents and noises at a fixed direction of the magnetic field in chiral systems, such as the edges of some quantum Hall liquids. We review the recent experimental and theoretical research, including the controversy on the microreversibility without time-reversal symmetry, consider the applications of fluctuation theorems to the physics of topological states of matter, and discuss open problems.
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We provide numerical evidence that the Onsager symmetry remains valid for systems subject to a spatially dependent magnetic field, in spite of the broken time-reversal symmetry. In addition, for the simplest case in which the field strength varies only in one direction, we analytically derive the result. For the generic case, a qualitative explanation is provided.
Here we present a model for a small system combined with an explicit entropy bath that is comparably small. The dynamics of the model is defined by a simple matrix, M. Each row of M corresponds to a macrostate of the system, e.g. net alignment, while the elements in the row represent microstates. The constant number of elements in each row ensures constant entropy, which allows reversible fluctuations, similar to information theory where a constant number of bits allows reversible computations. Many elements in M come from the microstates of the system, but many others come from the bath. Bypassing the bath states yields fluctuations that exhibit standard white noise; whereas with bath states the power spectral density varies as S(f)~1/f over a wide range of frequencies, f. Thus, the explicit entropy bath is the mechanism of 1/f noise in this model. Both forms of the model match Crooks fluctuation theorem exactly, indicating that the theorem applies not only to infinite reservoirs, but also to finite-sized baths. The model is used to analyze measurements of 1/f-like noise from a sub-micron tunnel junction.
We extend previous work to describe a class of fluctuation relations (FRs) that emerge as a consequence of symmetries at the level of stochastic trajectories in Markov chains. We prove that given such a symmetry, and for a suitable dynamical observable, it is always possible to obtain a FR under a biased dynamics corresponding to the so-called generalized Doob transform. The general transformations of the dynamics that we consider go beyond time-reversal or spatial isometries, and an implication is the existence of FRs for observables irrespective of their behaviour under time-reversal, for example for time-symmetric observables rather than currents. We further show how to deduce in the long-time limit these FRs from the symmetry properties of the generator of the dynamics. We illustrate our results with four examples that highlight the novel features of our work.
Topological insulators (TIs) are a new class of matter characterized by the unique electronic properties of an insulating bulk and metallic boundaries arising from non-trivial bulk band topology. While the surfaces of TIs have been well studied, the interface between TIs and semiconductors may not only be more technologically relevant but the interaction with non-topological states may fundamentally alter the physics. Here, we present a general model to show that such an interaction can lead to spin-momentum locked non-topological states, the Dirac cone can split in two, and the particle-hole symmetry can be fundamentally broken, along with their possible ramifications. Unlike magnetic doping or alloying, these phenomena occur without topological transitions or the breaking of time reversal symmetry. The model results are corroborated by first-principles calculations of the technologically relevant Bi$_2$Se$_3$ film van der Waals bound to a Se-treated GaAs substrate.
Spontaneous time-reversal symmetry (TRS) breaking plays an important role in studying strongly correlated unconventional superconductors. When the superconducting gap functions with different pairing symmetries compete, an Ising ($Z_2$) type symmetry breaking occurs due to the locking of the relative phase $Deltatheta_{12}$ via a second order Josephson coupling. The phase locking can take place even in the normal state in the phase fluctuation regime before the onset of superconductivity. If $Deltatheta_{12}=pmfrac{pi}{2}$, then TRS is broken, otherwise, if $Deltatheta_{12}=0$, or, $pi$, rotational symmetry is broken leading to a nematic state. In both cases, the order parameters possess a 4-fermion structure beyond the scope of mean-field theory. We employ an effective two-component $XY$-model assisted by a renormalization group analysis to address this problem. In addition, a quartetting, or, charge-``4e, superconductivity can also occur above $T_c$. Monte-Carlo simulations are performed and the results are in a good agreement with the renormalization group analysis. Our results provide useful guidance for studying novel symmetry breakings in strongly correlated superconductors.
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