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The high temperature limit of interacting spins is usually not associated with ordering or critical phenomena. Nevertheless, spontaneous fluctuations of a local spin polarization at equilibrium have nontrivial dynamics even in this limit. Here, we demonstrate that the spin noise power spectrum of these fluctuations can undergo discontinuous changes as a function of an external magnetic field. As a simple illustration, we consider a model of Ising-like long range spin-spin interactions with a transverse magnetic field as a control parameter. This system undergoes a phase transition associated with disappearance of the noise power peak responsible for the most detrimental decoherence effect of the interactions. \end{abstract}

Exactly solvable multistate Landau-Zener (MLZ) models are associated with families of operators that commute with the MLZ Hamiltonians and depend on time linearly. There can also be operators that satisfy the integrability conditions with the MLZ Hamiltonians but depend on time quadratically. We show that, among the MLZ systems, such time-quadratic operators are much more common. We demonstrate then that such operators generally lead to constraints on the independent variables that parametrize the scattering matrix. We show how such constraints lead to asymptotically exact expressions for the transition probabilities in the adiabatic limit of a three-level MLZ model. New fully solvable MLZ systems are also found., Comment: 12 pages, 9 figures

We study photon emission by an ensemble of two-level systems, with strong inhomogeneous broadening and coupled to a cavity mode whose frequency has linear time-dependence. The analysis shows that, regardless the distribution of energy level splittings, a sharp phase transition occurs between the weak and strong cooperative emission phases near a critical photonic frequency sweeping rate. The associated scaling exponent is determined. We suggest that this phase transition can be observed in an ensemble of negatively charged NV centers in diamond interacting with a microwave half-wavelength cavity mode even in the regime of weak coupling and at strong disorder of two-level splittings., Comment: 5 pages, 4 figures

We explore an unusual type of quantum matter that can be realized by qubits having different physical origin. Interactions in this matter are described by essentially different coupling operators for all qubits. We show that at least the simplest such models, which can be realized with localized states in Dirac materials, satisfy integrability conditions that we use to describe pseudospin dynamics in a linearly time-dependent magnetic field. Generalizing to an arbitrary number of qubits, we construct a spin Hamiltonian, which we call the gamma-magnet. This system does not conserve polarization of any spin and the net spin polarization. Nevertheless, for arbitrarily strong interactions, nonadiabatic dynamics, and any initial eigenstate, we find that quantum interference suppresses spin-flips. This behavior resembles many-body localization but occurs in phase space of many spins rather than real space. This effect may not have a counterpart in classical physics and can be a signature of a new type of spin ordering, which is different from both disordered spin glasses and ordered phases of spin lattices., Comment: 10 pages, 4 figures

We solve a model that has basic features that are desired for quantum annealing computations: entanglement in the ground state, controllable annealing speed, ground state energy separated by a gap during the whole evolution, and a programmable computational problem that is encoded by parameters of the Ising part of the spin Hamiltonian. Our solution enables exact nonperturbative characterization of final nonadiabatic excitations, including a scaling of their number with the annealing rate and the system size. We prove that quantum correlations can accelerate computations and, at the end of the annealing protocol, lead to the perfect Gibbs distribution of all microstates., Comment: 10 pages, 9 figures, Phys. Rev. Lett. (2018)

We use scanning optical magnetometry to study the broadband frequency spectra of spontaneous magnetization fluctuations, or "magnetization noise", in an archetypal ferromagnetic film that can be smoothly tuned through a spin reorientation transition (SRT). The SRT is achieved by laterally varying the magnetic anisotropy across an ultrathin Pt/Co/Pt trilayer, from the perpendicular to in-plane direction, via graded Ar$^+$ irradiation. In regions exhibiting perpendicular anisotropy, the power spectrum of the magnetization noise, $S(\nu)$, exhibits a remarkably robust $\nu^{-3/2}$ power law over frequencies $\nu$ from 1~kHz to 1~MHz. As the SRT region is traversed, however, $S(\nu)$ spectra develop a steadily-increasing critical frequency, $\nu_0$, below which the noise power is spectrally flat, indicating an evolving low-frequency cutoff for magnetization fluctuations. The magnetization noise depends strongly on applied in- and out-of-plane magnetic fields, revealing local anisotropies and also a field-induced emergence of fluctuations in otherwise stable ferromagnetic films. Finally, we demonstrate that higher-order correlators can be computed from the noise. These results highlight broadband spectroscopy of thermodynamic fluctuations as a powerful tool to characterize the interplay between thermal and magnetic energy scales, and as a means of characterizing phase transitions in ferromagnets.

The recent discovery of excellent thermoelectric properties and topological surface states in SnTe-based compounds has attracted extensive attention in various research areas. Indium doped SnTe is of particular interest because, depending on the doping level, it can either generate resonant states in the bulk valence band leading to enhanced thermoelectric properties, or induce superconductivity that coexists with topological states. Here we report on the vapor deposition of In-doped SnTe nanowires and the study of their surface oxidation and thermoelectric properties. The nanowire growth is assisted by Au catalysts, and their morphologies vary as a function of substrate position and temperature. Transmission electron microscopy characterization reveals the formation of amorphous surface in single crystalline nanowires. X-ray photoelectron spectroscopy studies suggest that the nanowire surface is composed of In2O3, SnO2, Te and TeO2 which can be readily removed by argon ion sputtering. Exposure of the cleaned nanowires to atmosphere yields rapid oxidation of the surface within only one minute. Characterizations of electrical conductivity {\sigma}, thermopower S, and thermal conductivity \k{appa} were performed on the same In-doped nanowire which shows suppressed {\sigma} and \k{appa} but enhanced S yielding an improved thermoelectric figure of merit ZT than the undoped SnTe., Comment: Substantial revisions; accepted for publication in Nanoscale

The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this resource can be used to accelerate information-processing without relying on entanglement or any other type of quantum correlations. In fact, there are computational problems that can be solved much faster, in comparison to currently used classical schemes, by saving intermediate information in nonorthogonal states of just a single qubit. There are also error correction strategies that protect such computations., Comment: 5 pages, 2 figures

We derive a set of constraints, which we will call hierarchy constraints (HCs), on scattering amplitudes of an arbitrary multistate Landau-Zener model (MLZM). The presence of additional symmetries can transform such constraints into nontrivial relations between elements of the transition probability matrix. This observation can be used to derive complete solutions of some MLZMs or, for models that cannot be solved completely, to reduce the number of independent elements of the transition probability matrix., Comment: 16 pages, 12 figures, Phys. Rev. A (2017)

Direct measurements of spin fluctuations are becoming the mainstream approach for studies of complex condensed matter, molecular, nuclear, and atomic systems. This review covers recent progress in the field of optical Spin Noise Spectroscopy (SNS) with an additional goal to establish an introduction into its theoretical foundations. Various theoretical techniques that have been recently used to interpret results of SNS measurements are explained alongside with examples of their applications.

We discuss the effect of external noisy magnetic fields on mesoscopic spin fluctuations that can be probed in semiconductors and atomic vapors by means of optical spin noise spectroscopy (SNS). We show that conventional arguments of the law of large numbers do not apply to spin correlations induced by external fields, namely, the magnitude of the 4th order spin cumulant grows as $\sim N^2$ with the number $N$ of observed spins, i.e. it is not suppressed in comparison to the 2nd order cumulant. This allows us to design a simple experiment to measure the 4th order cumulant of spin fluctuations in an atomic system near thermodynamic equilibrium and develop quantitative theory that explains all observations., Comment: 9 pages, 7 figures

We predict quantized Imbert-Fedorov, Goos-H\"anchen, and photonic spin Hall shifts for light beams impinging on a graphene-on-substrate system in an external magnetic field. In the quantum Hall regime the Imbert-Fedorov and photonic spin Hall shifts are quantized in integer multiples of the fine structure constant $\alpha$, while the Goos- H\"anchen ones in multiples of $\alpha^2$. We investigate the influence on these shifts of magnetic field, temperature, and material dispersion and dissipation. An experimental demonstration of quantized beam shifts could be achieved at terahertz frequencies for moderate values of the magnetic field., Comment: Correction of typos, title change, and updated references. 5 pages, 4 figures

We identify a nontrivial 4-state Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. The model describes an experimentally accessible system of two interacting qubits, such as a localized state in a Dirac material with both valley and spin degrees of freedom or a singly charged quantum dot (QD) molecule with spin orbit coupling. Application of the linearly time-dependent magnetic field induces a sequence of quantum level crossings with possibility of interference of different trajectories in a semiclassical picture. We argue that this system satisfies the criteria of integrability in the multistate Landau-Zener theory, which allows us to derive explicit exact analytical expressions for the transition probability matrix. We also argue that this model is likely a special case of a larger class of solvable systems, and present a 6-state generalization as an example., Comment: 7 pages, 5 figures

Higher order time-correlators of spontaneous spin fluctuations reveal the information about spin interactions. We argue that in a broad class of spin systems one can justify a phenomenological approach to explore such correlators. Thus, we predict that the 3rd and 4th order spin cumulants are described by a universal function that can be parametrized by a small set of parameters. We show that the fluctuation theorem constrains this function so that such correlators are fully determined by lowest nonlinear corrections to the free energy and the mean and variance of microscopic spin currents. We also provide an example of microscopic calculations for conduction electrons., Comment: 5 pages with supplementary materials, 2 Figs

We consider a localized electronic spin controlled by a circularly polarized optical beam and an external magnetic field. When the frequency of the beam is tuned near an optical resonance with a continuum of higher energy states, effective magnetic fields are induced on the two-level system via the Inverse Faraday Effect. We explore the process in which the frequency of the beam is made linearly time-dependent so that it sweeps through the optical resonance, starting and ending at the values far away from it. In addition to changes of spin states, Kramers-Kronig relations guarantee that a localized electron can also escape into a continuum of states. We argue that probabilities of transitions between different possible electronic states after such a sweep of the optical frequency can be found exactly regardless the shape of the resonance. We also discuss extension of our results to multistate systems., Comment: 12 pages, 6 figures

We identify a nontrivial multistate Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. In the semiclassical picture, this model features the possibility of interference of different trajectories that connect the same initial and final states. Hence, transition probabilities are generally not described by the incoherent successive application of the Landau-Zener formula. We discuss reasons for integrability of this system and provide numerical tests of the suggested expression for the transition probability matrix., Comment: 6 pages, 3 figures

We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form $\hat{H}(t) = \hat{A} +\hat{B} t + \hat{C}/t$, where $t$ is time and $\hat{A}$, $\hat{B}$, $\hat{C}$ are Hermitian $N\times N$ matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at $t \rightarrow -\infty$. This allows one to continue such solutions analytically to $t \rightarrow +\infty$, and connect their asymptotic behavior at $t \rightarrow -\infty$ and $t \rightarrow +\infty$. This property becomes particularly useful when a model shows additional discrete symmetries. In particular, we derive a number of simple exact constraints and explicit expressions for scattering probabilities in such systems., Comment: 16 pages, 7 figures

The control of discrete quantum states in solids and their use for quantum information processing is complicated by the lack of a detailed understanding of the mechanisms responsible for qubit decoherences. For spin qubits in semiconductor quantum dots, phenomenological models of decoherence currently recognize two Basic stages; fast ensemble dephasing due to the coherent precession of spin qubits around nearly static but randomly distributed hyperfine fields and a much slower process of irreversible relaxation of spin qubit polarization due to dynamics of the nuclear spin bath induced by complex many-body interaction effects. We unambiguosly demonstrate that such a view on decoherence is greatly oversimplified; the relaxation of a spin qubit state is determined by three rather than two basic stages. The additional stage corresponds to the effect of coherent dephasing processes that occur in the nuclear spin bath that manifests itself by a relatively fast but incomplete non-monotonous relaxation of the central spin polarization at intermediate timescales. This observation changes our understanding of the electron spin qubit decoherence mechanisms in solid state systems.

Per the fluctuation-dissipation theorem, the information obtained from spin fluctuation studies in thermal equilibrium is necessarily constrained by the system's linear response functions. However, by including weak radiofrequency magnetic fields, we demonstrate that intrinsic and random spin fluctuations even in strictly unpolarized ensembles \emph{can} reveal underlying patterns of correlation and coupling beyond linear response, and can be used to study non-equilibrium and even multiphoton coherent spin phenomena. We demonstrate this capability in a classical vapor of $^{41}$K alkali atoms, where spin fluctuations alone directly reveal Rabi splittings, the formation of Mollow triplets and Autler-Townes doublets, ac Zeeman shifts, and even nonlinear multiphoton coherences., Comment: 5 pages, 4 figures

We develop a theory for optical Faraday rotation noise in two-dimensional Dirac materials. In contrast to spin noise in conventional semiconductors, we find that the Faraday rotation fluctuations are influenced not only by spins but also the valley degrees of freedom attributed to intervalley scattering processes. We illustrate our theory with two-dimensional transition metal dichalcogenides and discuss signatures of spin and valley noise in the Faraday noise power spectrum. We propose optical Faraday noise spectroscopy as a technique for probing both spin and valley relaxation dynamics in two-dimensional Dirac materials., Comment: 5 pages, 2 figures

We derive an exact solution of an explicitly time-dependent multichannel model of quantum mechanical nonadiabatic transitions. Our model corresponds to the case of a single linear diabatic energy level interacting with a band of an arbitrary N states, for which the diabatic energies decay with time according to the Coulomb law. We show that the time-dependent Schroedingier equation for this system can be solved in terms of Meijer functions whose asymptotics at a large time can be compactly written in terms of elementary functions that depend on the roots of an Nth order characteristic polynomial. Our model can be considered a generalization of the Demkov-Osherov model. In comparison to the latter, our model allows one to explore the role of curvature of the band levels and diabatic avoided crossings., Comment: 18 pages, 3 figures

We obtain the exact expression for the matrix of nonadiabatic transition probabilities in the model of three interacting states with a time-dependent Hamiltonian. Unlike other known solvable Landau-Zener-like problems, our solution is generally expressed in terms of hypergeometric functions that have relatively complex behavior, e.g. the obtained transition probabilities may show multiple oscillations as functions of parameters of the model Hamiltonian., Comment: 12 pages, 3 figures

Here we suggest a novel hybrid spin noise spectroscopy technique, which is sensitive to the spin Hall effect. It is shown that, while the standard spin-spin correlation function is not sensitive to the spin Hall effect, spin-transverse voltage and transverse voltage-voltage correlation functions provide the missing sensitivity being linear and quadratic in the spin Hall coefficient, respectively. The correlation between transverse voltage and spin fluctuations appears as a result of spin-charge coupling fundamental for the spin Hall effect. We anticipate that the proposed method could find applications in the studies of spin-charge coupling in semiconductors.

We derive an exact solution of an explicitly time-dependent multichannel model of quantum mechanical nonadiabatic transitions. In the limit N >>1, where N is the number of states, we find that the survival probability of the initially populated state remains finite despite an almost arbitrary choice of a large number of parameters. This observation proves that quantum mechanical nonadiabatic transitions among a large number of states can effectively keep memory about the initial state of the system. This property can lead to a strongly non-ergodic behavior even in the thermodynamic limit of some systems with a broad distribution of coupling constants and the lack of energy conservation., Comment: 11 pages, 8 figures

We show that distinct topological phases of the band structure of a non-Hermitian Hamiltonian can be classified with elements of the braid group. As the proof of principle, we consider the non-Hermitian evolution of the statistics of nonequilibrium stochastic currents. We show that topologically nontrivial phases have detectable properties, including the emergence of decaying oscillations of parity and state probabilities, and discontinuities in the steady state statistics of currents., Comment: 4+ pages, 4 figures, published in PRE as a Rapid Communication. See http://pre.aps.org/abstract/PRE/v87/i5/e050101

We determine transition probabilities in two exactly solvable multistate Landau-Zener (LZ) models and discuss applications of our results to the theory of dynamic passage through a phase transition in the dissipationless quantum mechanical regime. In particular, we show that statistics of particles in a new phase demonstrate scaling behavior. Our results also reveal a symmetry that we claim is a property of a large class of multistate LZ models, whose explicit solutions are not presently known. We support our arguments by direct numerical simulations., Comment: 8 pages, 7 figures

We explore methods to use thermostatically controlled loads (TCLs), such as water heaters and air conditioners, to provide ancillary services by assisting in balancing generation and load. We show that by adding simple imbedded instructions and a small amount of memory to temperature controllers of TCLs, it is possible to design open-loop control algorithms capable of creating short-term pulses of demand response without unwanted power oscillations associated with temporary synchronization of the TCL dynamics. By moving a small amount of intelligence to each of the end point TCL devices, we are able to leverage our knowledge of the time dynamics of TCLs to shape the demand response pulses for different power system applications. A significant benefit of our open-loop method is the reduction from two-way to one-way broadcast communication which also eliminates many basic consumer privacy issues. In this work, we focus on developing the algorithms to generate a set of fundamental pulse shapes that can subsequently be used to create demand response with arbitrary profiles. Demand response control methods, such as the one developed here, open the door to fast, nonperturbative control of large aggregations of TCLs., Comment: 36 pages, 14 figures

Strain-induced gradients of local electric fields in semiconductor quantum dots can couple to the quadrupole moments of nuclear spins. We develop a theory describing the influence of this quadrupolar coupling (QC) on the spin correlators of electron and hole "central" spins localized in such dots. We show that when the QC strength is comparable to or larger than the hyperfine coupling strength between nuclei and the central spin, the relaxation rate of the central spin is strongly enhanced and can be exponential. We demonstrate a good agreement with recent experiments on spin relaxation in hole-doped (In,Ga)As self-assembled quantum dots., Comment: 6 pages, 7 figures

The problem of how single "central" spins interact with a nuclear spin bath is essential for understanding decoherence and relaxation in many quantum systems, yet is highly nontrivial owing to the many-body couplings involved. Different models yield widely varying timescales and dynamical responses (exponential, power-law, Gaussian, etc). Here we detect the small random fluctuations of central spins in thermal equilibrium (holes in singly-charged (In,Ga)As quantum dots) to reveal the timescales and functional form of bath-induced spin relaxation. This spin noise indicates long (400 ns) spin correlation times at zero magnetic field, that increase to $\sim$5 $\mu$s as hole-nuclear coupling is suppressed with small (100 G) applied fields. Concomitantly, the noise lineshape evolves from Lorentzian to power-law, indicating a crossover from exponential to inverse-log dynamics., Comment: 4 pages & 4 figures, + 8 pages supplemental material

We derive the exact equality, referred to as the fluctuation relation for heat engines (FRHE), that relates statistics of heat extracted from one of the two heat baths and the work per one cycle of a heat engine operation. Carnot's inequality of classical thermodynamics follows as a direct consequence of the FRHE., Comment: 3 pages, 1 figure

We present a new class of fluctuation relations, to which we will refer as Fluctuation Relations for Current Components (FRCCs). FRCCs can be used to estimate system parameters when complete information about nonequilibrium many-body electron interactions is unavailable. We show that FRCCs are often robust in the sense that they do not depend on some basic types of electron interactions and some quantum coherence effects., Comment: 8 pages; Phys. Rev. B (2011)

We consider stochastic motion of a particle on a cyclic graph with arbitrarily periodic time dependent kinetic rates. We demonstrate duality relations for statistics of currents in this model and in its continuous version of a diffusion in one dimension. Our duality relations are valid beyond detailed balance constraints and lead to exact expressions that relate statistics of currents induced by dual driving protocols. We also show that previously known no-pumping theorems and some of the fluctuation relations, when they are applied to cyclic graphs or to one dimensional diffusion, are special consequences of our duality., Comment: 2 figure, 6 pages (In twocolumn). Accepted by JSTAT

We discuss a non-equilibrium statistical system on a graph or network. Identical particles are injected, interact with each other, traverse, and leave the graph in a stochastic manner described in terms of Poisson rates, possibly dependent on time and instantaneous occupation numbers at the nodes of the graph. We show that under the assumption of constancy of the relative rates, the system demonstrates a profound statistical symmetry, resulting in geometric universality of the statistics of the particle currents. This phenomenon applies broadly to many man-made and natural open stochastic systems, such as queuing of packages over the internet, transport of electrons and quasi-particles in mesoscopic systems, and chains of reactions in bio-chemical networks. We illustrate the utility of our general approach using two enabling examples from the two latter disciplines., Comment: 15 pages, 5 figures

We demonstrate that the counting statistics of currents in periodically driven ergodic stochastic systems can show sharp changes of some of its properties in response to continuous changes of the driving protocol. To describe this effect, we introduce a new topological phase factor in evolution of the moment generating function which is akin to the topological geometric phase in evolution of a periodically driven quantum mechanical system with time-reversal symmetry. This phase leads to the prediction of a sign change for the difference of the probabilities to find even and odd number particles transferred in a stochastic system in response to cyclic evolution of control parameters. The driving protocols that lead to such a sign change should enclose specific degeneracy points in the space of control parameters. The relation between topology of the paths in the control parameter space and the sign changes can be described in terms of the first Stiefel-Whitney class., Comment: 8 pages, 3 figures

We generalize the concept of the geometric phase in stochastic kinetics to a noncyclic evolution. Its application is demonstrated on kinetics of the Michaelis-Menten reaction. It is shown that the nonperiodic geometric phase is responsible for the correction to the Michaelis-Menten law when parameters, such as a substrate concentration, are changing with time. We apply these ideas to a model of chemical reactions in a bacterial culture of a growing size, where the geometric correction qualitatively changes the outcome of the reaction kinetics., Comment: 11 pages

We explore quantization of the response of a molecular motor to periodic modulation of control parameters. We formulate the Pumping-Quantization Theorem (PQT) that identifies the conditions for robust integer quantized behavior of a periodically driven molecular machine. Implication of PQT on experiments with catenane molecules are discussed., Comment: 7 pages, 4 figures. J. Chem. Phys. Communications (in press)

We propose a spintronic device to generate spin polarization in a mesoscopic region by purely electric means. We show that the spin Hall effect in combination with the stirring effect are sufficient to induce measurable spin polarization in a closed geometry. Our device structure does not require the application of magnetic fields, external radiation or ferromagnetic leads, and can be implemented in standard semiconducting materials.

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.

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)

We propose a universal approach for analysis and fast simulations of stiff stochastic biochemical kinetics networks, which rests on elimination of fast chemical species without a loss of information about mesoscopic, non-Poissonian fluctuations of the slow ones. Our approach, which is similar to the Born-Oppenheimer approximation in quantum mechanics, follows from the stochastic path integral representation of the full counting statistics of reaction events (also known as the cumulant generating function). In applications with a small number of chemical reactions, this approach produces analytical expressions for moments of chemical fluxes between slow variables. This allows for a low-dimensional, interpretable representation of the biochemical system, that can be used for coarse-grained numerical simulation schemes with a small computational complexity and yet high accuracy. As an example, we consider a chain of biochemical reactions, derive its coarse-grained description, and show that the Gillespie simulations of the original stiff system, the coarse-grained simulations, and the full analytical treatment are in an agreement, but the coarse-grained simulations are three orders of magnitude faster than the Gillespie analogue., Comment: 29 pages, 8 figures

We formulate an exact result, which we refer to as the pumping restriction theorem (PRT). It imposes strong restrictions on the currents generated by periodic driving in a generic dissipative system with detailed balance. Our theorem unifies previously known results with the new ones and provides a universal nonperturbative approach to explore further restrictions on the stochastic pump effect in non-adiabatically driven systems., Comment: 4 pages, 5 figures

We develop a new interpretation of the geometric phase in evolution with a non-Hermitian real value Hamiltonian by relating it to the angle developed during the parallel transport along a closed curve by a unit vector triad in the 3D-Minkovsky space. We also show that this geometric phase is responsible for the anholonomy effects in stochastic processes considered in [N. A. Sinitsyn and I. Nemenman, EPL {\bf 77}, 58001 (2007)], and use it to derive the stochastic system response to periodic parameter variations., Comment: 10 pages 2 figures

We propose a method, which enables precise control of magnetic patterns, relying only on the fundamental properties of the wire and the choice of the path in the controlled parameter space but not on the rate of motion along this path. Possible experimental realizations of this mechanism are discussed. In particular, we show that the domain walls in magnetic nanowires can be translated by rotation of the magnetic easy axis, or by applying pulses of magnetic field directed transverse to the magnetic easy axis., Comment: 4 pages, 4 figures

In Phys. Rev. Lett. {\bf 66}, 847 (1991), T. B. Kepler and M. L. Kagan derived a geometric phase shift in dissipative limit cycle evolution. This effect was considered as an extension of the geometric phase in classical mechanics. We show that the converse is also true, namely, this geometric phase can be identified with the classical mechanical Hannay angle in an extended phase space. Our results suggest that this phase can be generalized to a stochastic evolution with an additional noise term in evolution equations.