Quasistationary states and the range of pair interactions

"Quasistationary" states are approximately time independent out of equilibrium states which have been observed in a variety of systems of particles interacting by long-range interactions. We investigate here the conditions of their occurrence for a generic pair interaction V(r→∞)~1/r(γ) with γ>0, in d>1 dimensions. We generalize analytic calculations known for gravity in d=3 to determine the scaling parametric dependences of their relaxation rates due to two-body collisions, and report extensive numerical simulations testing their validity. Our results lead to the conclusion that, for γd-1 it is conditioned on the short distance properties of the interaction, requiring the presence of a sufficiently large soft core in the interaction potential.     

Spin glasses and other lattice systems with long range interactions

We study classical lattice systems, in particular real spin glasses with Ruderman-Kittel interactions and dipole gases, with interactions of very long (non-summable) range but variable sign. Using the Kac-Siegert representation of such systems and Brascamp-Lieb inequalities we are able to establish detailed properties of the high-temperature phase, such as decay of connected correlations, for these systems.     

Nonlinear damping in spin systems: long range spin-spin interactions

The effective field theory of nonlinear damping for strongly interacting spins driven by external fields and weakly coupled to a bath is derived starting from the microscopic dynamics. The use of a block-spin model with long range spin-spin interactions makes it possible to treat the spin dynamics exactly and to eliminate the microscopic degrees of freedom. The results are presented in form of a nonlinear integro-differential equation for the time and space dependent magnetization. This equation is of memory type, applies to spin-spin interactions of any symmetry and is valid for inhomogeneous external fields of arbitrary strength and time dependence. For an isotropic ferromagnet in weak and slow external fields the general integro-differential equation is shown to reduce to a differential equation of motion of Landau-Lifshitz-Bloch type.This work was performed within a program of the Sonderforschungsbereich 185 Nichlineare Dynamik Frankfurt-Darmstadt     

Majorana edge states in interacting one-dimensional systems

We show that one-dimensional electron systems in the proximity of a superconductor that support Majorana edge states are extremely susceptible to electron-electron interactions. Strong interactions generically destroy the induced superconducting gap that stabilizes the Majorana edge states. For weak interactions, the renormalization of the gap is nonuniversal and allows for a regime in which the Majorana edge states persist. We present strategies of how this regime can be reached.     

Twisted injectivity in projected entangled pair states and the classification of quantum phases

We introduce a class of projected entangled pair states (PEPS) which is based on a group symmetry twisted by a 3-cocycle of the group. This twisted symmetry is expressed as a matrix product operator (MPO) with bond dimension greater than 1 and acts on the virtual boundary of a PEPS tensor. We show that it gives rise to a new standard form for PEPS from which we construct a family of local Hamiltonians which are gapped, frustration-free and include fixed points of the renormalization group flow. Based on this insight, we advance the classification of 2D gapped quantum spin systems by showing how this new standard form for PEPS determines the emergent topological order of these local Hamiltonians. Specifically, we identify their universality class as Dijkgraaf–Witten topological quantum field theory (TQFT).     

Variable range hopping in two-dimensional systems of interacting electrons

Computer modeling of the variable-range-hopping (VRH) conductivity in two-dimensional systems has been done by a kinetic Monte Carlo method, which includes some new elements. Study of the temperature dependence of the conductivity, testing of the different scaling relations, and study of the size effect show the detailed validity of the Efros-Shklovskii theory of the VRH in the system of interacting electrons. It has also been shown that simultaneous transitions of many electrons are not important. The reasons for disagreement with previous computational works are thoroughly analyzed.     

Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits

We present and discuss the derivation of a nonlinear nonlocal integrodifferential equation for the macroscopic time evolution of the conserved order parameter (r, t) of a binary alloy undergoing phase segregation. Our model is ad-dimensional lattice gas evolving via Kawasaki exchange with respect to the Gibbs measure for a Hamiltonian which includes both short-range (local) and long-range (nonlocal) interactions. The nonlocal part is given by a pair potential ^dJ(|x–y|), >0 x and y in ^d, in the limit 0. The macroscopic evolution is observed on the spatial scale ^–1 and time scale ^–2, i.e., the density (r, t) is the empirical average of the occupation numbers over a small macroscopic volume element centered atr=x. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (Part II) we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.     

Langevin dynamics of a π4-model with long range interactions

The Dominicis-Peliti generating functional (GF) method is used for the investigation of a Langevin dynamics of the π⁴-model: the symmetric double-well on-site potential and the infinite range interparticle interaction. We limit ourselves to the range above the temperature of the second order phase transition. The role of the 1/N-fluctuations (where N is the number of particles) is systematically investigated by using the steepest descent method. It is shown that the functional Legendre transformation directly results in the kinetic equation for the complete correlation function. Although this equation resembles the mode coupling equations used to describe the glass transition, it is qualitatively different. The solutions of this non-linear equation are investigated. It is shown that 1/N-fluctuations do not result in a breaking or ergodicity if the mean-field correlator is ergodic. On the other hand, if the mean-field correlator is nonergodic (e.g. if the time is much less than the inverse Kramers rate) then 1/N-fluctuations restore the ergodicity with characteristic relaxation time proportional to N.     

Effect of long range coulomb interactions on the mott transition

We reconsider the Mott transition problem in the presence of long range Coulomb interactions. Using an extended dynamical mean field theory (DMFT) that sums an important class of diagrams absent in ordinary DMFT, we show that in the presence of Coulomb interactions, the zero temperature Mott transition is, as envisioned by Mott, discontinuous in two and three dimensions.     

Time evolution of infinite classical systems with singular,long range,two body interactions

Existence of dynamics for infinitely many hard-spheres inv dimensions is proven in a set of full equilibrium measure.Singular unbounded perturbations are considered with pair potentials diverging as (x – a)^–, >2 anda is the hard-core diameter. Long range forces are allowed with potentials decreasing at infinity asx , <v. The result corrects and generalizes a proof given in a previous paper by the same authors.Research partially supported by a CNR fellowship Posit. 204530.Research partially supported by a CNR fellowship.     

Mesoscopic fluctuations of the local density of states in interacting electron systems

We review our recent theoretical results for mesoscopic fluctuations of the local density of states in the presence of electron–electron interaction. We focus on the two specific cases: (i) a vicinity of interacting critical point corresponding to an Anderson–Mott transition, and (ii) a vicinity of non-interacting critical point in the presence of a weak electron–electron attraction. In both cases, strong mesoscopic fluctuations of the local density of states exist.     

Decoupling of long range interactions and temporally first cause: a toy model

Although the question of the unification of the gravitational and electromagnetic interactions has been obscured by the unification of the electromagnetic and nuclear interactions, SU(2) gravitational gauge degrees have been recently unified to the U(1) electromagnetic degrees. If the resulting tracks of charges which mediate the unifying Yang-Mills field are assumed to induce a (dilation) scale invariance on the space-time geometry, the decoupling of these long range interactions, which takes place via a U(1) symmetry (periodic time) break, could be related to the onset of an initial singularity and origin of (linear) time.     

Quasi long range order in two-dimensional Bose systems

A microscopic derivation of quasi long range order in two-dimensional Bose systems is given using Jastrow variational theory in the paired phonon model.     

Relaxation and localization in interacting quantum maps

Quantum relaxation is studied in coupled quantum baker's maps. The classical systems are exactly solvable Kolmogorov systems, for which the exponential decay to equilibrium is known. They model the fundamental processes of transport in classically chaotic phase space. The quantum systems, in the absence of global symmetry, show a marked saturation in the level of transport, as the suppression of diffusion in the quantum kicked rotor, and eigenfunction localization in the position basis. In the presence of a global symmetry we study another model that has classically an identical decay to equilibrium, but-quantally shows resonant transport, no saturation, and large fluctuations around equilibrium. We generalize the quantization to finite multibaker maps. As a byproduct we introduce some simple models of quantal tunneling between classically chaotic regions of phase space.     

Stationary and quasi-stationary waves in even-order dissipative systems

A new equation was recently suggested by Rudenko and Robsman [1] for describing the nonlinear wave propagation in scattering media that are characterized by weak sound signal attenuation proportional to the fourth power of frequency. General self-similar properties of the solutions to this equation were studied. It was shown that stationary solutions to this equation in the form of a shock wave exhibit unusual oscillations around the shock front, as distinct from the classical Burgers equation. Here, similar solutions are studied in detail for nonlinear waves in even-order dissipative media; namely, the solutions are compared for the media with absorption proportional to the second, fourth, and sixth powers of frequency. Based on the numerical results and the self-similar properties of the solutions, the fine structure of the shock front of stationary waves is studied for different absorption laws and magnitudes. It is shown that the amplitude and number of oscillations appearing in the stationary wave profile increase with increasing power of the frequency-dependent absorption term. For initial disturbances in the form of a harmonic wave and a pulse, quasi-stationary solutions are obtained at the stage of fully developed discontinuities and the evolution of the profile and width of the shock wave front is studied. It is shown that the smoothening of the shock front in the course of wave propagation is more pronounced when the absorption law is quadratic in frequency.     

Energy transport in boundary driven quantum spin systems: One-way street phenomenon in models with long range interactions

We address the investigation of non trivial properties of the energy current in boundary driven XXZ quantum spin models. In specific, we focus on the occurrence of the one-way street phenomenon in asymmetrical chains, a phenomenon stronger than rectification, which establishes the existence of a unique way for the energy current in the absence of external magnetic field, that is, the magnitude and direction of the energy flow does not change as we invert the baths at the boundaries. For general target polarizations at the boundaries, we show that such a phenomenon holds in the presence of long range interactions, ingredient which increases the flow and the rectification in chains of classical oscillators, and so, of interest in the study of manipulation and control of the energy flow.     

Coexistence of the superconducting condensate and the quasi-stationary states of hole pairs

The formation of bound states in the case of a direct Coulomb repulsion between two holes whose reciprocal effective mass tensor has principal values of opposite signs is considered as a possible mechanism of high-T _C superconductivity. The study of the specific features of the scattering amplitude shows that, under certain conditions, in addition to the quasi-stationary states, states with a negative attenuation are possible, which corresponds to the tendency toward the formation of a hole pair condensate. The coexistence of the quasi-stationary states and the condensate qualitatively agrees with the phase diagram of p-type doped high-T _C superconducting cuprates.     

Splitting of a Cooper pair by a pair of Majorana bound states

We propose a method to probe the nonlocality of a pair of Majorana bound states by crossed Andreev reflection, which is the injection of an electron into one bound state followed by the emission of a hole by the other (equivalent to the splitting of a Cooper pair). We find that, at sufficiently low excitation energies, this nonlocal scattering process dominates over local Andreev reflection involving a single bound state. As a consequence, the low-temperature and low-frequency fluctuations deltaI(i) of currents into the two bound states i=1, 2 are maximally correlated: deltaI_1deltaI_2[over ]=deltaI_i(2).[over ].