Searcharxiv⌕ Search

arXiv subjects

Daniel Ueltschi

Publications and source records attributed to Daniel Ueltschi.

53 records · Page 3Linked to original sources
arXiv2009

Rigorous Upper Bound on the Critical Temperature of Dilute Bose Gases

We prove exponential decay of the off-diagonal correlation function in the two-dimensional homogeneous Bose gas when a^2 ρis small and the temperature T satisfies T > 4 πρ/ \ln |\ln(a^2ρ). Here, a is the scattering length of the repulsive interaction potential and ρis the density. To leading order in a^2 ρ, this bound agrees with the expected critical temperature for superfluidity. In the three-dimensional Bose gas, exponential decay is proved when ΔT_c / T_c^0 > 5 \sqrt{a ρ^{1/3}}, where T_c^0 is the critical temperature of the ideal gas. While this condition is not expected to be sharp, it gives a rigorous upper bound on the critical temperature for Bose-Einstein condensation.

cond-mat.stat-mech↗
arXiv2008

The model of interacting spatial permutations and its relation to the Bose gas

The model of spatial permutations is related to the Feynman-Kac representation of the Bose gas. The transition to infinite cycles corresponds to Bose-Einstein condensation. We review the general setting and some results, and we derive a multi-body interaction between permutation jumps, that is due to the original interactions between quantum particles.

cond-mat.stat-mech↗
arXiv2008

Spatial random permutations and infinite cycles

We consider systems of spatial random permutations, where permutations are weighed according to the point locations. Infinite cycles are present at high densities. The critical density is given by an exact expression. We discuss the relation between the model of spatial permutations and the ideal and interacting quantum Bose gas.

math-ph↗
arXiv2007

On a model of random cycles

We consider a model of random permutations of the sites of the cubic lattice. Permutations are weighted so that sites are preferably sent onto neighbors. We present numerical evidence for the occurrence of a transition to a phase with infinite, macroscopic cycles.

cond-mat.stat-mech↗
arXiv2006

Feynman cycles in the Bose gas

We study the lengths of the cycles formed by trajectories in the Feynman-Kac representation of the Bose gas. We discuss the occurrence of infinite cycles and their relation to Bose-Einstein condensation.

math-ph↗
arXiv2006

The relation between Feynman cycles and off-diagonal long-range order

The usual order parameter for the Bose-Einstein condensation involves the off-diagonal correlation function of Penrose and Onsager, but an alternative is Feynman's notion of infinite cycles. We present a formula that relates both order parameters. We discuss its validity with the help of rigorous results and heuristic arguments. The conclusion is that infinite cycles do not always represent the Bose condensate.

cond-mat.stat-mech↗
arXiv2006

Mott transition in lattice boson models

We use mathematically rigorous perturbation theory to study the transition between the Mott insulator and the conjectured Bose-Einstein condensate in a hard-core Bose-Hubbard model. The critical line is established to lowest order in the tunneling amplitude.

math-ph↗
arXiv2005

Cluster expansions and correlation functions

A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecky-Preiss criterion. Expressions and estimates for correlation functions are also presented. The results are applied to systems of interacting classical and quantum particles, and to a lattice polymer model.

math-ph↗
arXiv2004

Hund's rule and metallic ferromagnetism

We study tight-binding models of itinerant electrons in two different bands, with effective on-site interactions expressing Coulomb repulsion and Hund's rule. We prove that, for sufficiently large on-site exchange anisotropy, all ground states show metallic ferromagnetism: They exhibit a macroscopic magnetization, a macroscopic fraction of the electrons is spatially delocalized, and there is no energy gap for kinetic excitations.

cond-mat.str-el↗
arXiv2004

Statistical Mechanics of Thermodynamic Processes

In this note we describe some results concerning non-relativistic quantum systems at positive temperature and density confined to macroscopically large regions of physical space which are under the influence of some local, time-dependent external forces. We are interested in asymptotic properties of such systems.

math-ph↗
arXiv2004

Segregation in the asymmetric Hubbard model

We study the `asymmetric' Hubbard model, where hoppings of electrons depend on their spin. For strong interactions and sufficiently asymmetric hoppings, it is proved that the ground state displays phase separation away from half-filling. This extends a recent result obtained with Freericks and Lieb for the Falicov-Kimball model. It is based on estimates for the sum of lowest eigenvalues of the discrete Laplacian in arbitrary domains.

math-ph↗
arXiv2003

Dissipative Transport: Thermal Contacts and Tunnelling Junctions

The general theory of simple transport processes between quantum mechanical reservoirs is reviewed and extended. We focus on thermoelectric phenomena, involving exchange of energy and particles. Entropy production and Onsager relations are relevant thermodynamic notions which are shown to emerge from the microscopic description. The theory is illustrated on the example of two reservoirs of free fermions coupled through a local interaction. We construct a stationary state and determine energy- and particle currents with the help of a convergent perturbation series. We explicitly calculate several interesting quantities to lowest order, such as the entropy production, the resistance, and the heat conductivity. Convergence of the perturbation series allows us to prove that they are strictly positive under suitable assumptions on the interaction between the reservoirs.

math-ph↗
arXiv2002

A self-avoiding walk with attractive interactions

A self-avoiding walk with small attractive interactions is described here. The existence of the connective constant is established, and the diffusive behavior is proved using the method of the lace expansion.

math.PR↗
arXiv2002

Segregation in the Falicov-Kimball model

The Falicov-Kimball model is a simple quantum lattice model that describes light and heavy electrons interacting with an on-site repulsion; alternatively, it is a model of itinerant electrons and fixed nuclei. It can be seen as a simplification of the Hubbard model; by neglecting the kinetic (hopping) energy of the spin up particles, one gets the Falicov-Kimball model. We show that away from half-filling, i.e. if the sum of the densities of both kinds of particles differs from 1, the particles segregate at zero temperature and for large enough repulsion. In the language of the Hubbard model, this means creating two regions with a positive and a negative magnetization. Our key mathematical results are lower and upper bounds for the sum of the lowest eigenvalues of the discrete Laplace operator in an arbitrary domain, with Dirichlet boundary conditions. The lower bound consists of a bulk term, independent of the shape of the domain, and of a term proportional to the boundary. Therefore, one lowers the kinetic energy of the itinerant particles by choosing a domain with a small boundary. For the Falicov-Kimball model, this corresponds to having a single `compact' domain that has no heavy particles.

math-ph↗
arXiv1999

Analyticity in Hubbard models

The Hubbard model describes a lattice system of quantum particles with local (on-site) interactions. Its free energy is analytic when βt is small, or βt^2/U is small; here, βis the inverse temperature, U the on-site repulsion and t the hopping coefficient. For more general models with Hamiltonian H = V + T where V involves local terms only, the free energy is analytic when β||T|| is small, irrespectively of V. The Gibbs state exists in the thermodynamic limit, is exponentially clustering and thermodynamically stable. These properties are rigorously established in this paper.

cond-mat.stat-mech↗