Ground-state properties of a supersolid in RPA

We investigate the newly discovered supersolid phase by solving in random-phase approximation the anisotropic Heisenberg model of the hard-core boson ⁴He lattice at zero temperature. We include nearest and next-nearest neighbor interactions and calculate exactly all pair correlation functions in a cumulant decoupling scheme. We demonstrate the importance of vacancies and interstitials in the formation of the supersolid phase. The supersolid phase is characterised by strong quantum fluctuations which are taken into account rigorously. Furthermore we confirm that the superfluid to supersolid transition is triggered by a collapsing roton minimum however is stable against spontaneously induced superflow, i.e. vortex creation.     

Evolution of edge states in topological superfluids during the quantum phase transition

The quantum phase transition between topological and nontopological insulators or between fully gapped superfluids/superconductors can occur without closing the gap. We consider the evolution of the Majorana edge states on the surface of topological superconductor during transition to the topologically trivial superconductor on example of non-interacting Hamiltonian describing spin-triplet superfluid ³He-B. In conventional situation when the gap is nullified at the transition, the spectrum of Majorana fermions shrinks and vanishes after the transition to the trivial state. If the topological transition occurs without the gap closing, the Majorana fermion spectrum disappears by escaping to ultraviolet, where the Green’s function approaches zero. This demonstrates the close connection between the topological transition without closing the gap and zeroes in the Green’s function. Similar connection takes place in interacting systems where zeroes may occur due to interaction.     

Localization of Excitations near a Thin Structured Spacer between Linear and Nonlinear Crystals

It has been shown that localized and semi-localized stationary states exist near a thin structured defect layer between a linear medium and a Kerr nonlinear medium. Localized states are described by a monotonically decreasing amplitude of the field on the both sides of the interface between the media. Semilocalized states are characterized by the field that has the form of a standing wave in the linear medium and decreases monotonically in the nonlinear medium. Kerr media with self-focusing and defocusing are considered. The proposed model is described by a system of the linear and nonlinear Schrödinger equations with a specific potential simulating a thin structured defect layer. It has been shown that localized and semi-localized states exist in different energy ranges in the case of contact of the linear medium with the self-focusing medium. In the case of contact of the linear medium with the defocusing medium, two types of localized and semi-localized states differing in energy and field profile can exist in different energy ranges. In particular cases, expressions for energies of states of these types have been obtained and conditions of their applicability have been indicated.     

Superfluid density in a two-dimensional model of supersolid

We study in 2-dimensions the superfluid density of periodically modulated states in the framework of the mean-field Gross-Pitaevskiǐ model of a quantum solid. We obtain a full agreement for the superfluid fraction between a semi-theoretical approach and direct numerical simulations. As in 1-dimension, the superfluid density decreases exponentially with the amplitude of the particle interaction. We discuss the case when defects are present in this modulated structure. In the case of isolated defects (e.g. dislocations) the superfluid density only shows small changes. Finally, we report an increase of the superfluid fraction up to 50% in the case of extended macroscopical defects. We show also that this excess of superfluid fraction depends on the length of the complex network of grain boundaries in the system.     

Oscillations in ultrasonic attenuation near a phase transition

It is shown that the oscillations in ultrasonic attenuation observed in KH₂PO₄ near phase transition temperature cannot be due to velocity changes and interference of a coherent source with the echo as suggested by Steinitz et al. recently.     

Melting curve of 4He: no sign of a supersolid transition down to 10 mK

We have measured the melting curve of 4He in the temperature range from 10 to 400 mK with the accuracy of about 0.5 micro bar. Crystals of different quality show the expected T4 dependence in the range from 80 to 400 mK without any sign of the supersolid transition, and the coefficient is in excellent agreement with available data on the sound velocity in liquid 4He and on the Debye temperature of solid 4He. Below 80 mK, we have observed a small deviation from T4 dependence, which, however, cannot be attributed to the supersolid transition, because instead of decrease the entropy of the solid rather remains constant, about 2.5 x 10(-6) R.     

Critical field enhancement near a superconductor-insulator transition

We have discovered a phenomenon where the orbital pair breaking effect is reduced, if not eliminated. It appears as a striking enhancement in the upper critical field H(c2) for (TMTSF)2PF6 and a strong upward curvature in the critical field versus temperature in the region of pressure-temperature phase space near the superconductor-spin density wave insulator boundary. A simple model based on self-consistently dividing the superconductor into layers explains the observations remarkably well and provides a unique way around orbital frustration and toward higher critical fields.     

Elastic anomalies near a surface-induced phase transition

An analysis is made of the influence of elastic degrees of freedom on a surface-induced phase transition. It is found that elastic interactions give rise to a nonlinear correction to the boundary conditions for the order parameter, with the result that the surface transition is of the second order despite the fact that a first order phase transition occurs in the bulk. The propagation of Rayleigh waves near such a transition is discussed.     

Collective dynamics near a phase transition in confined fluids

We performed molecular dynamics simulations in the microcanonical ensemble (MEMD) for a "simple" fluid confined between two solid substrates. From the calculation of the intermediate scattering function F(k( parallel ),t) and through the memory function formalism, we extract material ( i.e. transport and thermodynamics) coefficients in the vicinity of the liquid-gas phase transition. Our results show that approaching the limit of stability ( i.e. the spinodal), the dynamics of the system changes markedly.     

Nonlinear percolation near a metal-insulator transition in regular textures

Current percolation in weakly nonlinear two-dimensional periodic structures near a metal-insulator transition is studied. It is shown that the nonlinear conductivity exhibits critical behavior as a function of the density of the insulating and superconducting inclusions. The possibility of experimentally observing the effects predicted is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 521–524 (10 April 1997)     

Atomic radiative transition probabilities in a continuous medium

A simple quantization procedure is applied to the electromagnetic radiation field in a nondissipative, weakly dispersive continuous medium. The resulting operator expressions for the electric and magnetic field strengths are used to study the influence of the dielectric and magnetic properties of the medium on the Einstein coefficients for spontaneous and stimulated radiative transitions of single atoms or molecules embedded in the medium. The expressions obtained are consistent with detailed-balance considerations.     

Conduction through a quantum dot near a singlet-triplet transition

Kondo effect in the vicinity of a singlet-triplet transition in a vertical quantum dot is considered. This system is shown to map onto a special version of the two-impurity Kondo model. At any value of the control parameter, the system has a Fermi-liquid ground state. Explicit expressions for the linear conductance as a function of the control parameter and temperature T are obtained. At T = 0, the conductance reaches the unitary limit approximately 4e(2)/h at the triplet side of the transition, and decreases with the increasing distance to the transition at the singlet side. At finite temperature, the conductance exhibits a peak near the transition point.     

The synchronization transition in correlated oscillator populations

The synchronization transition of correlated ensembles of coupled Kuramoto oscillators on sparse random networks is investigated. Extensive numerical simulations show that correlations between the native frequencies of adjacent oscillators on the network systematically shift the critical point as well as the critical exponents characterizing the transition. Negative correlations imply an onset of synchronization for smaller coupling, whereas positive correlations shift the critical coupling towards larger interaction strengths. For negatively correlated oscillators the transition still exhibits critical behaviour similar to that of the all-to-all coupled Kuramoto system, while positive correlations change the universality class of the transition depending on the correlation strength. Crucially, the paper demonstrates that the synchronization behaviour is not only determined by the coupling architecture, but also strongly influenced by the oscillator placement on the coupling network.     

Loschmidt echo near a dynamical phase transition in a Bose-Einstein condensate

We show that the quantum Loschmidt echo can be employed to characterize the dynamical phase transition, from a tunnelling phase to a self-trapping phase, of a Bose-Einstein condensate in a double-well potential. The echo is found to have a relatively fast decay in the transition region, with a Gaussian decay in the self-trapping phase and a stretched exponential decay in the tunnelling phase.