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In thermodynamics a macroscopic state of a system results from a number of its microscopic states. This number is given by the exponent of the system's entropy $\exp(S)$. In non-interacting systems with discrete energy spectra, such as large scale quantum dots, $S$ as a function of the temperature has usually a plateau shape with integer values of $\exp(S)$ on these plateaus. Plateaus with non-integer values of $\exp(S)$ are fundamentally forbidden and would be thermodynamically infeasible. Here we investigate the entropy of a non-interacting quantum dot coupled via tunneling to normal metals with continuum spectra as well as to topological superconductors. We show that the entropy may have non-integer plateaus if the topological superconductors support weakly overlapping Majorana bound states. This brings a fundamental change in the thermodynamics of the quantum dot whose specific heat $c_V$ acquires low temperature Majorana peaks which should be absent according to the conventional thermodynamics. We also provide a fundamental thermodynamic understanding of the transport properties, such as the linear conductance. In general our results show that the thermodynamics of systems coupled to Majorana modes represents a fundamental physical interest with diverse applications depending on versatility of possible coupling mechanisms., Comment: 8 pages, 11 figures

Conventionally the Cherenkov sound is governed by {\it orbital} degrees of freedom and is excited by {\it supersonic} particles. Additionally, it usually has a {\it forward} nature with a conic geometry known as the Cherenkov cone whose axis is oriented {\it along} the {\it supersonic} particle motion. Here we predict Cherenkov sound of a unique nature entirely resulting from the electronic {\it spin} degree of freedom and demonstrate a fundamentally distinct Cherenkov effect originating from essentially {\it subsonic} electrons in two-dimensional gases with both Bychkov-Rashba and Dresselhaus spin-orbit interactions. Specifically, we show that the axis of the conventional {\it forward} Cherenkov cone gets a nontrivial {\it quarter-turn} and at the same time the sound distribution strongly localizes around this rotated axis being now {\it orthogonal} to the {\it subsonic} particle motion. Apart from its fundamentally appealing nature, the orthogonal Cherenkov sound could have applications in planar semiconductor technology combining spin and acoustic phenomena to develop, {\it e.g.}, acoustic amplifiers or sound sources with a flexible spin dependent orientation of the sound propagation., Comment: 7 pages, 4 figures

Physical systems with co-existence and interplay of processes featuring distinct spatio-temporal scales are found in various research areas ranging from studies of brain activity to astrophysics. Complexity of such systems makes their theoretical and experimental analysis technically and conceptually challenging. Here, we discover that radiation of partially mode-locked fibre lasers, while being stochastic and intermittent on short time scale, exhibits periodicity and long scale correlations over slow evolution from one round trip to another. The evolution mapping of intensity auto-correlation function allows us to reveal variety of spatio-temporal coherent structures and to experimentally study their symbiotic co-existence with stochastic radiation. Our measurements of interactions of noisy pulses over a time scale of thousands of non-linear lengths demonstrate that they have features of incoherent temporal solitons. Real-time measurements of spatio-temporal intensity dynamics are set to bring new insight into rich underlying nonlinear physics of practical active- and passive-cavity photonic systems.

Darboux integrability of semidiscrete and discrete 2D Toda lattices corresponding to Lie algebras of A and C series is proved., Comment: 23 pages

A general phenomenon of the Cherenkov radiation known in optics or acoustics of conventional materials is a formation of a forward cone of, respectively, photons or phonons emitted by a particle accelerated above the speed of light or sound in those materials. Here we suggest three-dimensional topological insulators as a unique platform to fundamentally explore and practically exploit the acoustic aspect of the Cherenkov effect. We demonstrate that applying an in-plane magnetic field to a surface of a three-dimensional topological insulator one may suppress the forward Cherenkov sound up to zero at a critical magnetic field. Above the critical field the Cherenkov sound acquires pure backward nature with the polar distribution differing from the forward one generated below the critical field. Potential applications of this asymmetric Cherenkov reverse are in design of low energy electronic devices such as acoustic ratchets or, in general, in low power design of electronic circuits with a magnetic field control of the direction and magnitude of the Cherenkov dissipation., Comment: published version; 6 pages, 5 figures

Topological insulators are currently of considerable interest due to peculiar electronic properties originating from helical states on their surfaces. Here we demonstrate that the sound excited by helical particles on surfaces of topological insulators has several exotic properties fundamentally different from sound propagating in non-helical or even isotropic helical systems. Specifically, the sound may have strictly forward propagation absent for isotropic helical states. Its dependence on the anisotropy of the realistic surface-states is of distinguished behavior which may be used as an alternative experimental tool to measure the anisotropy strength. Fascinating from the fundamental point of view backward, or anomalous, Cherenkov sound is excited above the critical angle $\pi/2$ when the anisotropy exceeds a critical value. Strikingly, at strong anisotropy the sound localizes into a few forward and backward beams propagating along specific directions., Comment: 9 pages, 15 figures

We analyze universal transport properties of a strongly interacting quantum dot in the Kondo regime when the quantum dot is placed in an external magnetic field. The quantum dot is described by the asymmetric Anderson model with the spin degeneracy removed by the magnetic field resulting in the Zeeman splitting. Using an analytical expression for the tunneling density of states found from a Keldysh effective field theory, we obtain in the whole energy range the universal differential conductance and analytically demonstrate its Fermi-liquid and logarithmic behavior at low- and high-energies, respectively, as a function of the magnetic field. We also show results on the zero temperature differential conductance as a function of the bias voltage at different magnetic fields as well as results on finite temperature effects out of equilibrium and at a finite magnetic field. The modern nonequilibrium experimental issues of the critical magnetic field, at which the zero bias maximum of the differential conductance starts to split into two maxima, as well as the distance between these maxima as a function of the magnetic field are also addressed., Comment: Published version; First submission to NJP: 27.03.2013; Second submission to NJP: 06.05.2013

We present a theory for the Kondo spin-1/2 effect in strongly correlated quantum dots. The theory is applicable at any temperature and voltage. It is based on a quadratic Keldysh effective action parameterized by a universal function. We provide a general analytical form for the tunneling density of states through this universal function for which we propose a simple microscopic model. We apply our theory to the highly asymmetric Anderson model with $U=\infty$ and describe its strong coupling limit, weak coupling limit and crossover region within a single analytical expression. We compare our results with numerical renormalization group in equilibrium and with a real-time renormalization group out of equilibrium and show that the universal shapes of the linear and differential conductance obtained in our theory and in these theories are very close to each other in a wide range of temperatures and voltages. In particular, as in the real-time renormalization group, we predict that at the Kondo voltage the differential conductance is equal to 2/3 of its maximum., Comment: 5 pages, 2 figures + supp.mat

Integrable cut-off constraints for semidiscrete Toda lattice are studied in this paper. Lax presentation for semidiscrete analog of the $C$-series Toda lattice is obtained. Nonlocal variables that allow to express symmetries of the infinite semidiscrete lattice are introduced and cut-off constraints or a certain type compatible with symmetries of the infinite lattice are classified., Comment: 15 pages

We develop a low-energy nonequilibrium field theory for weakly interacting quantum dots. The theory is based on the Keldysh field integral in the spin channel of the quantum dot described by the single impurity Anderson Hamiltonian. The effective Keldysh action is a functional of the Hubbard-Stratonovich magnetization field decoupling the quantum dot spin channel. We expand this action up to the second order with respect to the magnetization field, which allows to describe nonequilibrium interacting quantum dots at low temperatures and weak electron-electron interactions,up to the contacts-dot coupling energy. Besides its simplicity, an additional advantage of the theory is that it correctly describes the unitary limit giving the correct result for the conductance maximum. Thus our theory establishes an alternative simple method relevant for investigation of weakly interacting nonequilibrium nanodevices., Comment: published version

Kondo physics in nonequilibrium interacting nanoscale devices is an attractive fundamental many-particle phenomenon with a rich potential for applications. Due to enormous complexity its clear and flexible theory is still highly desirable. We develop a physically transparent analytical theory capable to correctly describe the Kondo effect in strongly interacting systems at temperatures close to and above the Kondo temperature. We derive a nonequilibrium Keldysh field theory valid for a system with any finite electron-electron interaction which is much stronger than the coupling of the system to contacts. Finite electron-electron interactions are treated involving as many slave-boson degrees of freedom as one needs for a concrete many-body system. In a small vicinity of the zero slave-bosonic field configuration weak slave-bosonic oscillations, induced by the dot-contacts tunneling, are described by an effective Keldysh action quadratic in the slave-bosonic fields. For clarity the theory is presented for the single impurity Anderson model but the construction of the Keldysh field integral is universal and applicable to systems with more complex many-body spectra., Comment: 5 pages, 2 figures

We present a {\it nonequilibrium nonperturbative} field theory for the Kondo effect in strongly interacting quantum dots at finite temperatures. Unifying the slave-boson representation with the Keldysh field integral an effective Keldysh action is derived and explored in the vicinity of the zero slave-bosonic field configuration. The theory properly reflects the essential features of the Kondo physics and at the same time significantly simplifies a field-theoretic treatment of the phenomenon, avoiding complicated saddle point analysis or 1/N expansions, used so far. Importantly, our theory admits a {\it closed analytical} solution which explains the mechanism of the Kondo effect in terms of an interplay between the real and imaginary parts of the slave-bosonic self-energy. It thus provides a convenient nonperturbative building block, playing the role of a "free propagator", for more advanced theories. We finally demonstrate that already this simplest possible field theory is able to correctly reproduce experimental data on the Kondo peak observed in the differential conductance, correctly predicts the Kondo temperature and, within its applicability range, has the same universal temperature dependence of the conductance as the one obtained in numerical renormalization group calculations., Comment: published version

The Cherenkov effect is a well known phenomenon in the electrodynamics of fast charged particles passing through transparent media. If the particle is faster than the light in a given medium, the medium emits a forward light cone. This beautiful phenomenon has an acoustic counterpart where the role of photons is played by phonons and the role of the speed of light is played by the sound velocity. In this case the medium emits a forward sound cone. Here, we show that in a system with spin-orbit interactions in addition to this {\it normal} Cherenkov sound there appears an {\it anomalous} Cherenkov sound with forward and {\it backward} sound propagation. Furthermore, we demonstrate that the transition from the normal to anomalous Cherenkov sound happens in a {\it singular} way at the Cherenkov cone angle. The detection of this acoustic singularities therefore represents an alternative experimental tool for the measurement of the spin-orbit coupling strength., Comment: published version

We investigate the Ruderman-Kittel-Kasuya-Yosida oscillations of the itinerant carrier spin density in a system where those oscillations appear only due to a finite distribution of a localized spin. The system represents a half-infinite one-dimensional quantum wire with a magnetic impurity located at its edge. In contrast to the conventional model of a point-like exchange interaction the itinerant carrier spin density oscillations in this system exist. We {\it analytically} demonstrate that when the radius of the exchange interaction is less than the wave length of the itinerant carriers living on the Fermi surface, the long range behavior of the oscillations is identical to the one taking place in the zero radius limit of the same exchange interaction but for an infinite one-dimensional quantum wire where, in comparison with the original half-infinite system, the mass of the itinerant carriers is {\it strongly} modified by the exchange interaction radius. On the basis of our analysis we make a suggestion on directionality of surface Ruderman-Kittel-Kasuya-Yosida interaction shown in recent experiments: we believe that in general the anisotropy of the Ruderman-Kittel-Kasuya-Yosida interaction could result not only from the anisotropy of the {\it Fermi surface} of itinerant carriers but also from the anisotropy of the {\it spin carrying atomic orbitals} of magnetic impurities., Comment: Published version, 6 pages, 4 figures

Traditionally the charge ratchet effect is considered as a consequence of either the spatial symmetry breaking engineered by asymmetric periodic potentials, or time asymmetry of the driving fields. Here we demonstrate that electrically and magnetically driven quantum dissipative systems with spin-orbit interactions represent an exception from this standard idea. In contrast to the so far well established belief, a charge ratchet effect appears when both the periodic potential and driving are symmetric. We show that the source of this paradoxical charge ratchet mechanism is the coexistence of quantum dissipation with the spin flip processes induced by spin-orbit interactions., Comment: 5 pages, 3 figures

This is an entry for the Gallery of Fluid Motion of the 62nd Annual Meeting of the APS-DFD (fluid dynamics videos). This video shows the three-dimensional time-dependent incremental spin-up of a thermally stratified fluid in a cylinder and in an annulus. The rigid bottom/side wall(s) are non-slip, and the upper surface is stress-free. All the surfaces are thermally insulated. The working fluid is water characterized by the kinematic viscosity $\nu$ and thermal diffusivity $\kappa$. Initially, the fluid temperature varies linearly with height and is characterized by a constant buoyancy frequency $N$, which is proportional to the density gradient. The system undergoes an abrupt change in the rotation rate from its initial value $\Omega_i $, when the fluid is in a solid-body rotation state, to the final value $\Omega_f$. Our study reveals a feasibility for transition from an axisymmetric initial circulation to non-axisymmetric flow patterns at late spin-up times.

Traditionally the charge ratchet effect is considered as a consequence of the extrinsic spatial asymmetry engineered by external asymmetric periodic potentials. Here we demonstrate that electrically and magnetically driven dissipative systems with spin-orbit interactions represent an exception from this standard idea. The charge and spin ratchet currents appear just due to the coexistence of quantum dissipation with the intrinsic spatial asymmetry of the spin-orbit coupling. The extrinsic spatial asymmetry is inessential., Comment: 4 pages, 3 figures

A non-interacting electron gas on a one-dimensional ring is considered at finite temperatures. The localized spin is embedded at some point on the ring and it is assumed that the interaction between this spin and the electrons is the exchange interaction being the basis of the Ruderman-Kittel-Kasuya-Yosida indirect exchange effect. When the number of electrons is large enough, it turns out that any small but finite interaction radius value can always produce an essential change of the spin density oscillations in comparison with the zero interaction radius traditionally used to model the Ruderman-Kittel-Kasuya-Yosida effect., Comment: 6 pages, 4 figures, early attempts to take into account the finite size of the ionic spin distribution in connection with Heusler alloys are now metioned