arXiv subjects

Markus Holzmann

Publications and source records attributed to Markus Holzmann.

At least 109 records · Page 6Linked to original sources

arXiv2008

Semiclassical theory of the quasi two-dimensional trapped Bose gas

We discuss the quasi two-dimensional trapped Bose gas where the thermal occupation of excited states in the tightly confined direction is small but remains finite in the thermodynamic limit. We show that the semiclassical theory describes very accurately the density profile obtained by Quantum Monte Carlo calculations in the normal phase above the Kosterlitz--Thouless temperature T_KT, but differs strongly from the predictions of strictly two-dimensional mean-field theory, even at relatively high temperature. We discuss the relevance of our findings for analyzing ultra-cold-atom experiments in quasi two-dimensional traps.

cond-mat.stat-mech↗

arXiv2007

Trial wave functions for High-Pressure Metallic Hydrogen

Many body trial wave functions are the key ingredient for accurate Quantum Monte Carlo estimates of total electronic energies in many electron systems. In the Coupled Electron-Ion Monte Carlo method, the accuracy of the trial function must be conjugated with the efficiency of its evaluation. We report recent progress in trial wave functions for metallic hydrogen implemented in the Coupled Electron-Ion Monte Carlo method. We describe and characterize several types of trial functions of increasing complexity in the range of the coupling parameter $1.0 \leq r_s \leq1.55$. We report wave function comparisons for disordered protonic configurations and preliminary results for thermal averages.

physics.comp-ph↗

arXiv2007

Kosterlitz-Thouless transition of the quasi two-dimensional trapped Bose gas

We present Quantum Monte Carlo calculations with up to N=576000 interacting bosons in a quasi two-dimensional trap geometry closely related to recent experiments with atomic gases. The density profile of the gas and the non-classical moment of inertia yield intrinsic signatures for the Kosterlitz--Thouless transition temperature T_KT. From the reduced one-body density matrix, we compute the condensate fraction, which is quite large for small systems. It decreases slowly with increasing system sizes, vanishing in the thermodynamic limit. We interpret our data in the framework of the local-density approximation, and point out the relevance of our results for the analysis of experiments.

cond-mat.stat-mech↗

arXiv2007

Condensate superfluidity and infrared structure: the Josephson relation

We derive the Josephson relation in a superfluid between the condensate density, the superfluid mass density, and the infrared structure of the single particle Green's function by means of diagrammatic perturbation theory. The derivation is valid for finite systems and two dimensions.

cond-mat.stat-mech↗

arXiv2006

Many-body wavefunctions for normal liquid $^3$He

We present new trial wave-functions which include 3-body correlations into the backflow coordinates and a 4-body symmetric potential. We show that our wavefunctions lower the energy enough to stabilize the ground state energies of normal liquid $^3$He in the unpolarized state at all pressures in agreement with experiment; however, quantitative discrepancies remain. Further, we include strong spin coupling into the Fermi liquid by adapting pairing wave functions. We demonstrate a new, numerically stable method to evaluate pairing functions which is also useful for Path Integrals calculations at low, but non-zero temperatures.

cond-mat.str-el↗

arXiv2006

The Finite Size Error in Many-body Simulations with long-Ranged Interactions

We discuss the origin of the finite size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random phase approximation at long wave lengths. The correction comes from contributions mainly determined by the organized collective oscillations of the interacting system. Finite size corrections, both on kinetic and potential energy, can be calculated within a single simulation. Results are presented for the electron gas and silicon.

cond-mat.other↗

arXiv2005

The Kosterlitz-Thouless-Berezinskii transition of homogeneous and trapped Bose gases in two dimensions

We derive the scaling structure of the Kosterlitz-Thouless-Berezinskii (KTB) transition temperature of a homogeneous Bose gas in two dimensions within diagrammatic perturbation theory. Approaching the system from above the transition, we calculate the critical temperature, $T_{KT}$, and show how the superfluid mass density emerges from Josephson's relation as an interplay between the condensate density in a finite size system, and the infrared structure of the single particle Green's function. We then discuss the trapped two-dimensional Bose gas, where the interaction changes the transition qualitatively from Bose-Einstein in an ideal gas to a KTB transition in the thermodynamic limit. We show that the transition temperature lies below the ideal Bose-Einstein transition temperature, and calculate the first correction in terms of the interparticle interactions. The jump of the total superfluid mass at the transition is suppressed in a trapped system.

cond-mat.other↗

arXiv2004

Coupled Electron Ion Monte Carlo Calculations of Atomic Hydrogen

We present a new Monte Carlo method which couples Path Integral for finite temperature protons with Quantum Monte Carlo for ground state electrons, and we apply it to metallic hydrogen for pressures beyond molecular dissociation. This method fills the gap between high temperature electron-proton Path Integral and ground state Diffusion Monte Carlo methods. Our data exhibit more structure and higher melting temperatures of the proton crystal than Car-Parrinello Molecular Dynamics results using LDA. We further discuss the quantum motion of the protons and the zero temperature limit.

cond-mat.stat-mech↗

arXiv2004

Optimized Periodic Coulomb Potential in Two Dimension

The 1/r Coulomb potential is calculated for a two dimensional system with periodic boundary conditions. Using polynomial splines in real space and a summation in reciprocal space we obtain numerically optimized potentials which allow us efficient calculations of any periodic (long-ranged) potential up to high precision. We discuss the parameter space of the optimized potential for the periodic Coulomb potential. Compared to the analytic Ewald potential, the optimized potentials can reach higher precisions by up to several orders of magnitude. We explicitly give simple expressions for fast calculations of the periodic Coulomb potential where the summation in reciprocal space is reduced to a few terms.

cond-mat.other↗

arXiv2004

Coupled Electron Ion Monte Carlo Calculations of Dense Metallic Hydrogen

We present a new Monte Carlo method which couples Path Integral for finite temperature protons with Quantum Monte Carlo for ground state electrons, and we apply it to metallic hydrogen for pressures beyond molecular dissociation. We report data for the equation of state for temperatures across the melting of the proton crystal. Our data exhibit more structure and higher melting temperatures of the proton crystal than Car-Parrinello Molecular Dynamics results. This method fills the gap between high temperature electron-proton Path Integral and ground state Diffusion Monte Carlo methods.

physics.comp-ph↗

arXiv2003

Bose-Einstein transition temperature in a dilute repulsive gas

We discuss certain specific features of the calculation of the critical temperature of a dilute repulsive Bose gas. Interactions modify the critical temperature in two different ways. First, for gases in traps, temperature shifts are introduced by a change of the density profile, arising itself from a modification of the equation of state of the gas (reduced compressibility); these shifts can be calculated simply within mean field theory. Second, even in the absence of a trapping potential (homogeneous gas in a box), temperature shifts are introduced by the interactions; they arise from the correlations introduced in the gas, and thus lie inherently beyond mean field theory - in fact, their evaluation requires more elaborate, non-perturbative, calculations. One illustration of this non-perturbative character is provided by the solution of self-consistent equations, which relate together non-linearly the various energy shifts of the single particle levels k. These equations predict that repulsive interactions shift the critical temperature (at constant density) by an amount which is positive, and simply proportional to the scattering length a; nevertheless, the numerical coefficient is difficult to compute. Physically, the increase of the temperature can be interpreted in terms of the reduced density fluctuations introduced by the repulsive interactions, which facilitate the propagation of large exchange cycles across the sample.

cond-mat↗

arXiv2002

Condensate density and superfluid mass density of a dilute Bose gas near the condensation transition

We derive, through analysis of the structure of diagrammatic perturbation theory, the scaling behavior of the condensate and superfluid mass density of a dilute Bose gas just below the condensation transition. Sufficiently below the critical temperature, $T_c$, the system is governed by the mean field (Bogoliubov) description of the particle excitations. Close to $T_c$, however, mean field breaks down and the system undergoes a second order phase transition, rather than the first order transition predicted in Bogoliubov theory. Both condensation and superfluidity occur at the same critical temperature, $T_c$ and have similar scaling functions below $T_c$, but different finite size scaling at $T_c$ to leading order in the system size. Through a simple self-consistent two loop calculation we derive the critical exponent for the condensate fraction, $2β\simeq 0.66$.

cond-mat.stat-mech↗

arXiv2001

Bose-Einstein transition in a dilute interacting gas

We study the effects of repulsive interactions on the critical density for the Bose-Einstein transition in a homogeneous dilute gas of bosons. First, we point out that the simple mean field approximation produces no change in the critical density, or critical temperature, and discuss the inadequacies of various contradictory results in the literature. Then, both within the frameworks of Ursell operators and of Green's functions, we derive self-consistent equations that include the dynamic correlations in the system and predict the change of the critical density. We argue that the dominant contribution to this change can be obtained within classical field theory and show that the lowest order correction introduced by interactions is linear in the scattering length, $a$, with a positive coefficient. Finally, we calculate this coefficient within various approximations, and compare with various recent numerical estimates.

cond-mat.stat-mech↗

arXiv2001

Non-analytic dependence of the transition temperature of the homogeneous dilute Bose gas on scattering length

We show that the shift in the transition temperature of the dilute homogeneous Bose gas is non-analytic in the scattering amplitude, $a$. The first correction beyond the positive linear shift in $a$ is negative and of order $a^2\ln a$. This non-universal non-analytic structure indicates how the discrepancies between numerical calculations at finite $a$ can be reconciled with calculations of the limit $a \to0$, since the linearity is apparent only for anomalously small $a$.

cond-mat.stat-mech↗

arXiv2001

Finite size scaling and the role of the thermodynamic ensemble in the transition temperature of a dilute Bose gas

We study the Bose-Einstein condensation phase transition in a weakly interacting gas through a perturbative analysis of finite systems. In both the grand canonical and the canonical ensembles, perturbation theory suffers from infrared divergences and cannot directly determine the transition temperature in the thermodynamic limit. However, in conjunction with finite size scaling, perturbation theory provides a powerful calculation tool. We implement it here to estimate a shift in the transition temperature in the canonical ensemble consistent with grand canonical calculations.

cond-mat.stat-mech↗

arXiv1999

Bogoliubov transformation for distinguishable particles

The Bogoliubov transformation is generally derived in the context of identical bosons with the use of ``second quantized'' a and $a^{\dagger}$ operators (or, equivalently, in field theory). Here, we show that the transformation, together with its characteristic energy spectrum, can also be derived within the Hilbert space of distinguishable particles, obeying Boltzmann statistics; in this derivation, ordinary dyadic operators play the role usually played by the a and $a^{\dagger}$ operators; therefore, breaking the symmetry of particle conservation is not necessary.

cond-mat.stat-mech↗

arXiv1999

Transition Temperature of the homogeneous, weakly interacting Bose gas

We present a Monte Carlo calculation for up to $N \sim 20 000$ bosons in 3 D to determine the shift of the transition temperature due to small interactions $a$. We generate independent configurations of the ideal gas. At finite $N$, the superfluid density changes by a certain correlation function in the limit $a \to 0$; the $N \to \infty$ limit is taken afterwards. We argue that our result is independent of the order of limits. Detailed knowledge of the non-interacting system for finite $N$ allows us to avoid finite-size scaling assumptions.

cond-mat.stat-mech↗

arXiv1999

The transition temperature of the dilute interacting Bose gas

We show that the critical temperature of a uniform dilute Bose gas must increase linearly with the s-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.

cond-mat.stat-mech↗