Finite-temperature Excitations Research Articles

Large-N Expansion for Condensation and Stability of Bose–Bose Mixtures at Finite Temperatures

The two-component mixture of Bose particles with short-range pairwise interaction at finite temperatures in three dimensions is considered. Particularly we examine, by means of the large-$N$ expansion technique, the stability of mixed state below the Bose-Einstein transition point and the temperature dependence of the condensate density for symmetric mixture of Bose gases. The presented analysis reveals the importance of finite-temperature excitations of the non-condensed particles in formation of the phase diagram of two-component Bose systems.

Non-vanishing zero-temperature normal density in holographic superfluids

The low energy and finite temperature excitations of a d + 1-dimensional system exhibiting superfluidity are well described by a hydrodynamic model with two fluid flows: a normal flow and a superfluid flow. In the vicinity of a quantum critical point, thermodynamics and transport in the system are expected to be controlled by the critical exponents and by the spectrum of irrelevant deformations away from the quantum critical point. Here, using gauge-gravity duality, we present the low temperature dependence of thermodynamic and charge transport coefficients at first order in the hydrodynamic derivative expansion in terms of the critical exponents. Special attention will be paid to the behavior of the charge density of the normal flow in systems with emergent infrared conformal and Lifshitz symmetries, parameterized by a Lifshitz dynamical exponent z > 1. When 1 ≤ z < d + 2, we recover (z = 1) and extend (z > 1) previous results obtained by relativistic effective field theory techniques. Instead, when z > d + 2, we show that the normal charge density becomes non-vanishing at zero temperature. An extended appendix generalizes these results to systems that violate hyperscaling as well as systems with generalized photon masses. Our results clarify previous work in the holographic literature and have relevance to recent experimental measurements of the superfluid density on cuprate superconductors.

Finite-temperature dynamical correlations for the dimerized spin- 12 chain

We use the density matrix renormalization group method (DMRG) to compute the frequency and momentum resolved spin-spin correlation functions of a dimerized spin-1/2 chain under a magnetic field at finite temperature. The spectral features strongly depend on the regime of the magnetic field. For increasing magnetic fields, the transitions from a gapped spin liquid phase to a Tomonaga-Luttinger liquid, and then to a totally polarized phase, can be identified in the spectra. Compared to the zero temperature case, the finite temperature excitations give rise to additional spectral features that we compute numerically and identify analytically as transitions from thermally excited states. We compute quantitatively the broadening of the dispersion of a single spin-flip excitation due to the temperature and find a strong asymmetric broadening. We discuss the consequences of these findings for neutron experiments on dimerized one dimensional quantum chains.

Finite-Temperature Micromagnetism

It is investigated how magnetic hysteresis is affected by finite-temperature excitations, using soft regions in hard-magnetic matrices as model systems. In lowest order, magnetization processes are described by the traditional approach of using finite-temperature materials constants such as K1 (T). Nanoscale excitations are usually small perturbations. For example, a Bloch summation over all magnon wave vectors shows that remanence is slightly enhanced, because long-wavelength excitations are suppressed. However, a reverse magnetic field enhances the effect of thermal excitations and causes a small reduction of the coercivity. To describe such effects, we advocate micromagnetic calculations where finite-temperature fluctuations are treated as small corrections to the traditional approach, as contrasted to full-scale Monte Carlo simulations.

Mechanical instabilities and structural phase transitions: The cubic to tetragonal transformation

A variety of technologically important crystalline phases are predicted by first-principles electronic structure methods to be mechanically unstable at 0 K, raising fundamental questions about the finite temperature excitations that stabilize these phases at high-temperature. Here, we show that anharmonic vibrational degrees of freedom can stabilize a cubic phase that is mechanically unstable at 0 K with respect to a tetragonal distortion. We develop an effective anharmonic strain Hamiltonian for a cubic lattice and parameterize its coefficients to first-principles calculations of the energy surface of TiH 2, a compound that undergoes a cubic to tetragonal transformation around 300 K and for which the cubic phase is predicted to be mechanically unstable. Monte Carlo simulations applied to the effective Hamiltonian predict a cubic to tetragonal phase transition and provide insight about the true nature of the high-temperature cubic phase.

Finite-temperature excitations of an inhomogeneous trapped Bose gas with Feshbach resonances

We derive and discuss the temperature dependence of the condensate and noncondensate density profile of a Bose-Einstein condensate gas with Feshbach resonance in a parabolic trap. These quantities are calculated self-consistently using the generalized Hartree-Fock-Bogoliubov (HFB) equations within the Bogoliubov approximation. At zero temperature, the HFB equation can be solved by means of a variation method that gives the low-excitation spectrum. Moreover, within the two-body collision theory, we estimate the relationship between the number of atoms in the condensate and the external magnetic field B. The result is in good agreement with data from recent experiments.

Finite-temperature excitations of Bose gases in anisotropic traps

The mode frequencies of a weakly interacting Bose gas in a magnetic trap are studied as a function of the anisotropy of the trap. As in earlier works, the generalized Hartree-Fock-Bogoliubov equations within the Popov approximation are used for our calculations. A feature of our work is the combined use of a mode expansion in a finite basis and a semiclassical approximation of the highly excited states. The results are applied to check the accuracy of the recently suggested equivalent zero temperature condensate approximation, which involves a much simpler model.

Finite-temperature excitations in a dilute Bose-condensed gas

We present a systematic account of several approximations for the Beliaev self-energies for a uniform dilute Bose gas at finite temperature. We discuss the first-order Popov approximation, which gives a phonon velocity which vanishes as n 0(T) , where n 0( T) is the Bose condensate density. We generalize this Popov approximation using a t-matrix calculated with self-consistent ladder diagrams. This analysis shows that this t-matrix becomes very temperature-dependent and vanishes at T c, in agreement with Bijlsma and Stoof (1995). Finally, we make a detailed study of the Beliaev–Popov (B–P) approximation for the self-energies which are second order in the t-matrix. We work out the contribution from each individual diagram and give formal expressions for the self-energies and the excitation energy spectrum valid at arbitrary temperature. Careful attention is given to all infrared-divergent contributions. We rederive the well-known T=0 result of Beliaev (1958) for long-wavelength excitations. The analogous evaluation of the finite-temperature B–P self-energies is given in the low-frequency and long-wavelength limit. The corrections to the chemical potential, excitation energy and damping are all found to be proportional to the temperature near T c. All infrared divergent terms are shown to cancel out in physical quantities in the long-wavelength limit at arbitrary temperatures.

Collective excitations of Bose-Einstein-condensed gases at finite temperatures

We have applied the Popov version of the Hartree-Fock-Bogoliubov (HFB) approximation to calculate the finite-temperature excitation spectrum of a Bose-Einstein condensate (BEC) of ${}^{87}\mathrm{Rb}$ atoms. For lower values of the temperature, we find excellent agreement with recently published experimental data for the JILA time-averaged orbiting potential trap. In contrast to recent comparison of the results of HFB-Popov theory with experimental condensate fractions and specific heats, there is disagreement of the theoretical and recent experimental results near the BEC phase transition temperature.

Finite Temperature Excitations of a Trapped Bose Gas

We present a detailed study of the temperature dependence of the condensate and noncondensate density profiles of a Bose-condensed gas in a parabolic trap. These quantitites are calculated self-consistently using the Hartree-Fock-Bogoliubov equations within the Popov approximation. Below the Bose-Einstein transition the excitation frequencies have a realtively weak temperature dependence even though the condensate is strongly depleted. As the condensate density goes to zero through the transition, the excitation frequencies are strongly affected and approach the frequencies of a noninteracting gas in the high temperature limit.

THERMODYNAMICS AND EXCITATIONS OF THE SUPERSYMMETRIC t-J MODEL

The free energy of the supersymmetric t-J model is expressed in terms of finite temperature excitations away from thermodynamic equilibrium. This reveals that the free energy has the form of noninteracting fermions with temperature dependent excitation spectra. We also discuss the ground state and zero temperature excitations.

Glueball-like screening masses in pure SU (3) at finite temperatures

We investigate the finite-temperature excitation spectrum in the gluon sector of SU (3) pure gauge theory through measurements of screening masses in correlations of loop operators. We develop the classification of such operators under the symmetry group of the “z- slice” . In the confined phase of the theory, we find that the spectrum dynamically realizes the zero-temperature symmetries. We observe a large thermal shift of the 0 ++ glueball mass. In the deconfined phase, the spectrum distinguishes between operators coupling to electrically and magnetically polarised gluon fields. The former yields a screening mass equal to the Wilson-line screening mass; the latter a method for the measurement of the magnetic mass in the high-temperature limit.

Path-integral Monte Carlo study of the hard-disk solid.

We present a study of the properties of the quantum two-dimensional hard-disk solid at finite temperatures using path-integral Monte Carlo simulations. We performed extensive simulations on systems with 64, 144, 256, 576, and 1024 disks. We used the image approximation for the high-temperature density matrix and ignored exchange effects. Despite the discontinuous nature of the hard-disk interaction, a long-wavelength harmonic theory provided a good model for the solid. This theory was used as a guide to study the long-range translational and orientational order of the solid at low but finite temperatures where the zero-point motion and finite-temperature excitations are both important. The properties we have computed include the particle displacements, structure factor, angular order, and density of topological defects. We compare these properties with those of the same system in the classical regime and at absolute zero, thus gaining some understanding for the crossover from classical to quantum behavior.

Finite-temperature excitations of the Toda lattice in the semiclassical regime

The finite-temperature excitations of a large Toda lattice in the semiclassical regime are analysed using the Bethe ansatz, and a physical interpretation is presented, showing clearly that the lattice phonon excitation corresponds to the Bethe ansatz hole, even in the classical limit at finite temperature. The authors' method gives a simple derivation of the formulae for excitation energies and momenta, which were first written down by Gruner-Bauer and Mertens (1988) from a consistency argument, and it suggests why solitons do not apparently contribute to the Toda lattice free energy.

Excitation spectrum of the Toda lattice for finite temperatures

For the Toda lattice, the integral equations of Yang and Yang are derived for the classical limit and their analytical solutions are given. The introduction of renormalized energies eventually leads to a finite temperature excitation spectrum of classical solitons and semiclassical phonons. The excitation energies are tested by a comparison of the group velocities for vanishing momentum with the sound velocity which can be calculated directly from the thermodynamics.

Excitations of a dense charged Bose gas at finite temperatures

Abstract We discuss the finite temperature excitation spectrum in a dense charged Bose-condensed gas (CBG), which is of interest in connection with the new high transition temperature oxide superconductors. The free Bose gas (RPA), and the 1-loop approximations for the proper, irreducible quantities are examined. We point out that while the plasmon excitation frequency is essentially temperature-independent in a dense CBG, its weight as a pole of the single particle Green functions decreases with the condensate fraction n 0 ( T ). At the same time, as the temperature increases, the single particle spectral weight shifts to strongly damped single-particle modes, which become free particles at T c . Thus we conclude that, in contrast to a dilute weakly interacting Bose gas with short-range interactions, the excitation spectrum of a CBG is more analogous to that in superfluid 4 He.

Finite-temperature excitation spectrum of many-body systems solvable by the Bethe ansatz

For certain integrable gas and lattice models in one dimension the Bethe ansatz lead to a formal description of the system as a spinless Fermi gas. The particle-hole structure of the zero-temperature excitations is generalized to finite temperatures. Dispersion and thermal distribution of the excitations are calculated, and tested for the Toda lattice.

Finite temperature excitations of the quantum sine-Gordon-massive Thirring model: Variation of the soliton mass with coupling constant and temperature.

For the quantum sine-Gordon--massive Thirring model at finite temperature, the relationship between the Bethe ansatz ``elementary excitations'' and physical excitations of the system is examined. The thermodynamic equations are written in terms of a set of dressed particles in the general case. We find that the recently predicted soliton mass discontinuity (on varying coupling strength at finite temperature) is not a real effect--the function exhibiting the discontinuity does not correspond to the mass of the soliton.

Isothermal Excitations of the Massive Thirring Model and the Quantum Sine-Gordon Model

the definition of Yang and Yang, 15) and the other being the isothermal excitation. In the present work, we investigate these two types of finite temperature excitations, in particular the latter one mainly, on the basis of the BA thermodynamics. As is well known, in the BA theory of the MT model and thE} QSG model the energy and the momentum of the pseudo-Fermi particles are given by using the rapidity param­ eter /3 through the relation e(/3)= moch/3 and k(/3)= mosh/3, respectively, where mo is the bare mass of the pseudo-particles. These pseudo-particles are grouped into various length of to form bound states. The rapidity parameters of the pseudo-particles of the strings are distributed in the complex rapidity plane with the common real value (which we denote a) and the equal distances along the imaginary axis. The allowed values of the pseudo-particle number of the string, which we denote nJ, are the Same as those of the XYZ model. On these bases we define the isothermal excitation energy in the following way: We add (or subtract) strings with fixed rapidities and lengths to the system, minimize the free

Finite-Temperature Excitations of the Classical Toda Chain

The finite-temperature excitation spectrum of the classical Toda lattice is obtained by numerical solution of the Bethe Ansatz. Bethe-Ansatz thermodynamics agrees exactly with known transfer-integral results. A soliton-phonon phenomenology is developed and its validity assessed with the Bethe-Ansatz spectrum as an exact standard. The phenomenology's intrinsic limitations become evident in a transition region, where a distinction between phonon and (nontopological) soliton is impossible.