Nonequilibrium thermodynamics as a gauge theory

We assume that markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential. A widely accepted expression for the total entropy production of a system arises as the simplest gauge-invariant completion of the time derivative of Gibbs's entropy. We show that transition rates can be given a simple physical characterization in terms of locally-detailed-balanced heat reservoirs. It follows that Clausius's measure of irreversibility along a cyclic transformation is a geometric phase. In this picture, the gauge symmetry arises as the arbitrariness in the choice of a prior probability. Thermostatics depends on the information that is disposable to an observer; thermodynamics does not.Comment: 6 pages. Non-fatal errors in eq.(6), eq.(26) and eq.(31) have been amende

Stochastic pump effect and geometric phases in dissipative and stochastic systems

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).Comment: Review. 35 pages. J. Phys. A: Math, Theor. (in press

Coordinate shift in the semiclassical Boltzmann equation and the anomalous Hall effect

We propose a gauge invariant expression for the side jump associated with scattering between particular Bloch states. Our expression for the side jump follows from the Born series expansion for the scattering T-matrix in powers of the strength of the scattering potential. Given our gauge invariant side jump expression, it is possible to construct a semiclassical Boltzmann theory of the anomalous Hall effect which expresses all previously identified contributions in terms of gauge invariant quantities and does not refer explicitly to off-diagonal terms in the density-matrix response.Comment: 6 pages, 1 fugure. submitted to PR

Fluctuation relations for heat engines in time-periodic steady states

A fluctuation relation for heat engines (FRHE) has been derived recently. In the beginning, the system is in contact with the cooler bath. The system is then coupled to the hotter bath and external parameters are changed cyclically, eventually bringing the system back to its initial state, once the coupling with the hot bath is switched off. In this work, we lift the condition of initial thermal equilibrium and derive a new fluctuation relation for the central system (heat engine) being in a time-periodic steady state (TPSS). Carnot's inequality for classical thermodynamics follows as a direct consequence of this fluctuation theorem even in TPSS. For the special cases of the absence of hot bath and no extraction of work, we obtain the integral fluctuation theorem for total entropy and the generalized exchange fluctuation theorem, respectively. Recently microsized heat engines have been realized experimentally in the TPSS. We numerically simulate the same model and verify our proposed theorems.Comment: 9 page

Formation of a National Assessment of the Probability of Investing in Fraudulent ICOs

The study covers such concepts as ICO and IPO, their characteristics, similarities and differences. A national estimate of the probability of investing in fraudulent ICOs has been formed. Also, the work is about comparing the likelihood of investing in fraudulent IPOs and ICO.     Keywords: cryptocurrency, block technology, ICO, IP

Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach

The anomalous Hall effect (AHE) is a consequence of spin-orbit coupling in a ferromagnetic metal and is related primarily to density-matrix response to an electric field that is off-diagonal in band index. For this reason disorder contributions to the AHE are difficult to treat systematically using a semi-classical Boltzmann equation approach, even when weak localization corrections are disregarded. In this article we explicitly demonstrate the equivalence of an appropriately modified semiclassical transport theory which includes anomalous velocity and side jump contributions and microscopic Kubo-Streda perturbation theory, with particular unconventional contributions in the semiclassical theory identified with particular Feynman diagrams when calculations are carried out in a band-eigenstate representation. The equivalence we establish is verified by explcit calculations for the case of the two-dimensional (2D) Dirac model Hamiltonian relevant to graphene.Comment: 17 pages, 13 figure

Quantum state preparation in circuit QED via Landau-Zener tunneling

We study a qubit undergoing Landau-Zener transitions enabled by the coupling to a circuit-QED mode. Summing an infinite-order perturbation series, we determine the exact nonadiabatic transition probability for the qubit, being independent of the frequency of the QED mode. Possible applications are single-photon generation and the controllable creation of qubit-oscillator entanglement.Comment: 7 pages, 3 figure

Edge states in a honeycomb lattice: effects of anisotropic hopping and mixed edges

We study the edge states in graphene in the presence of a magnetic field perpendicular to the plane of the lattice. Most of the works done so far discuss the edge states in either zigzag or armchair edge graphene considering an isotropic electron hopping. In practice, graphene can have mixture of armchair and zigzag edges and the electron hopping can be anisotropic, which is the subject of this article. We predict that the mixed edges smear the enhanced local density of states (LDOS) at E=0 of the zigzag edge and, on the other hand, the anisotropic hopping gives rise to the enhanced LDOS at E=0 in the armchair edge. The behavior of the LDOS can be studied using scanning tunneling microscopy (STM) experiments. We suggest that care must be taken while interpreting the STM data. It is because the clear distinction between the zigzag edge (enhanced LDOS at E=0) and armchair edge (suppressed LDOS at E=0) can be lost if the hopping is not isotropic and if the edges are mixed

Inverse Spin Hall Effect and Anomalous Hall Effect in a Two-Dimensional Electron Gas

We study the coupled dynamics of spin and charge currents in a two-dimensional electron gas in the transport diffusive regime. For systems with inversion symmetry there are established relations between the spin Hall effect, the anomalous Hall effect and the inverse spin Hall effect. However, in two-dimensional electron gases of semiconductors like GaAs, inversion symmetry is broken so that the standard arguments do not apply. We demonstrate that in the presence of a Rashba type of spin-orbit coupling (broken structural inversion symmetry) the anomalous Hall effect, the spin Hall and inverse spin Hall effect are substantially different effects. Furthermore we discuss the inverse spin Hall effect for a two-dimensional electron gas with Rashba and Dresselhaus spin-orbit coupling; our results agree with a recent experiment.Comment: 5 page