arXiv subjects

Andras Suto

Publications and source records attributed to Andras Suto.

31 records · Page 2Linked to original sources

arXiv2006

From bcc to fcc: interplay between oscillating long-range and repulsive short-range forces

This paper supplements and partly extends an earlier publication, Phys. Rev. Lett. 95, 265501 (2005). In $d$-dimensional continuous space we describe the infinite volume ground state configurations (GSCs) of pair interactions $\vfi$ and $\vfi+ψ$, where $\vfi$ is the inverse Fourier transform of a nonnegative function vanishing outside the sphere of radius $K_0$, and $ψ$ is any nonnegative finite-range interaction of range $r_0\leqγ_d/K_0$, where $γ_3=\sqrt{6}π$. In three dimensions the decay of $\vfi$ can be as slow as $\sim r^{-2}$, and an interaction of asymptotic form $\sim\cos(K_0r+π/2)/r^3$ is among the examples. At a dimension-dependent density $ρ_d$ the ground state of $\vfi$ is a unique Bravais lattice, and for higher densities it is continuously degenerate: any union of Bravais lattices whose reciprocal lattice vectors are not shorter than $K_0$ is a GSC. Adding $ψ$ decreases the ground state degeneracy which, nonetheless, remains continuous in the open interval $(ρ_d,ρ_d')$, where $ρ_d'$ is the close-packing density of hard balls of diameter $r_0$. The ground state is unique at both ends of the interval. In three dimensions this unique GSC is the bcc lattice at $ρ_3$ and the fcc lattice at $ρ_3'=\sqrt{2}/r_0^3$.

math-ph↗

arXiv2006

Equivalence of Bose-Einstein condensation and symmetry breaking

Based on a classic paper by Ginibre [Commun. Math. Phys. {\bf 8} 26 (1968)] it is shown that whenever Bogoliubov's approximation, that is, the replacement of a_0 and a_0^* by complex numbers in the Hamiltonian, asymptotically yields the right pressure, it also implies the asymptotic equality of |< a_0>|^2/V and < a_0^*a_0>/V in symmetry breaking fields, irrespective of the existence or absence of Bose-Einstein condensation. Because the former was proved by Ginibre to hold for absolutely integrable superstable pair interactions, the latter is equally valid in this case. Apart from Ginibre's work, our proof uses only a simple convexity inequality due to Griffiths.

math-ph↗

arXiv2006

Crystalline ground states for classical particles

Pair interactions whose Fourier transform is nonnegative and vanishes above a wave number K_0 are shown to give rise to periodic and aperiodic infinite volume ground state configurations (GSCs) in any dimension d. A typical three dimensional example is an interaction of asymptotic form cos(K_0 r)/r^4. The result is obtained for densities rho >= rho_d where rho_1=K_0/2pi, rho_2=(sqrt{3}/8)(K_0/pi)^2 and rho_3=(1/8sqrt{2})(K_0/pi)^3. At rho_d there is a unique periodic GSC which is the uniform chain, the triangular lattice and the bcc lattice for d=1,2,3, respectively. For rho>rho_d the GSC is nonunique and the degeneracy is continuous: Any periodic configuration of density rho with all reciprocal lattice vectors not smaller than K_0, and any union of such configurations, is a GSC. The fcc lattice is a GSC only for rho>=(1/6 sqrt{3})(K_0/pi)^3.

math-ph↗

arXiv2004

Normal and generalized Bose condensation in traps: One dimensional examples

We prove the following results. (i) One-dimensional Bose gases which interact via unscaled integrable pair interactions and are confined in an external potential increasing faster than quadratically undergo a complete generalized Bose-Einstein condensation (BEC) at any temperature, in the sense that a macroscopic number of particles are distributed on a o(N)number of one-particle states. (ii) In a one dimensional harmonic trap the replacement of the oscillator frequency ωby ω\ln N/N gives rise to a phase transition at a=\hbarωβ=1 in the noninteracting gas. For a<1 the limit distribution of n_0/N^a is exponential and /N^a tends to 1. For a>1 there is BEC with a condensate density /N going to 1-1/a. For a>=1, (\ln N/N)(n_0- ) is asymptotically distributed following Gumbel's law. For any a>0 the free energy is -(π^2/6aβ)N/\ln N+o(N/\ln N), with no singularity at a=1. (iii) In Model (ii) both above and below the critical temperature the the gas undergoes a complete generalized BEC, thus providing a coexistence of ordinary and generalized condensates below the critical point. (iv) Adding an interaction =o(N\ln N) to Model (ii) we prove that a complete generalized BEC occurs at all temperatures.

cond-mat.stat-mech↗

arXiv2004

Bose-Einstein condensation and symmetry breaking

Adding a gauge symmetry breaking field -ν\sqrt{V}(a_0+a_0^*) to the Hamiltonian of some simplified models of an interacting Bose gas we compute the condensate density and the symmetry breaking order parameter in the limit of infinite volume and prove Bogoliubov's asymptotic hypothesis \lim_{V\to\infty}< a_0>/\sqrt{V}={\rm sgn}ν\lim_{V\to\infty}\sqrt{< a_0^*a_0>/V} where the averages are taken in the ground state or in thermal equilibrium states. Letting νtend to zero in this equation we obtain that Bose-Einstein condensation occurs if and only if the gauge symmetry is spontaneously broken. The simplification consists in dropping the off-diagonal terms in the momentum representation of the pair interaction. The models include the mean field and the imperfect (Huang-Yang-Luttinger) Bose gas. An implication of the result is that the compressibility sum rule cannot hold true in the ground state of the one-dimensional mean-field Bose gas. Our method is based on a resolution of the Hamiltonian into a family of single-mode (k=0) Hamiltonians and on the analysis of the associated microcanonical ensembles.

cond-mat.stat-mech↗

arXiv2004

Correlation inequalities for noninteracting Bose gases

For a noninteracting Bose gas with a fixed one-body Hamiltonian H^0 independent of the number of particles we derive the inequalities _N < _{N+1}, _N < _N _N for i\neq j, \partial _N/\partial β>0 and ^+_N < _N. Here N_i is the occupation number of the ith eigenstate of H^0, βis the inverse temperature and the superscript + refers to adding an extra level to those of H^0. The results follow from the convexity of the N-particle free energy as a function of N.

math-ph↗

arXiv2003

Ab initio structure solution by charge flipping

In this paper we present an extremely simple structure solution method termed charge flipping. It works ab initio on high resolution x-ray diffraction data in the manner of Fourier recycling. The real space modification simply changes the sign of charge density below a threshold, while in reciprocal space the modification is the Fobs map without any weighting. We test the algorithm using synthetic data for a wide range of structures, analyse the solution statistics and check the quality of reconstruction. Finally, we reconsider mathematical aspects of the algorithm in detail, showing that in this chaotic iteration process the solution is a limit cycle and not a fixed point.

cond-mat↗

arXiv2003

Thermodynamic limit and proof of condensation for trapped bosons

We study condensation of trapped bosons in the limit when the number of particles tends to infinity. For the noninteracting gas we prove that there is no phase transition in any dimension, but in any dimension at any temperature the system is 100% condensated into the one-particle ground state. In the case of an interacting gas we show that for a family of suitably scaled pair interactions, the Gross-Pitaevskii scaling included, a less-than-100% condensation into a one-particle eigenstate, which may depend on the interaction strength, persists at all temperatures.

cond-mat.stat-mech↗

arXiv2003

Power-law bounds on transfer matrices and quantum dynamics in one dimension II

We establish quantum dynamical lower bounds for a number of discrete one-dimensional Schrödinger operators. These dynamical bounds are derived from power-law upper bounds on the norms of transfer matrices. We develop further the approach from part I and study many examples. Particular focus is put on models with finitely or at most countably many exceptional energies for which one can prove power-law bounds on transfer matrices. The models discussed in this paper include substitution models, Sturmian models, a hierarchical model, the prime model, and a class of moderately sparse potentials.

math-ph↗

arXiv2002

Exact eigenstates for contact interactions

We show that in d>1 dimensions the N-particle kinetic energy operator with periodic boundary conditions has symmetric eigenfunctions which vanish at particle encounters, and give a full description of these functions. In two and three dimensions they represent common eigenstates of bosonic Hamiltonians with any kind of contact interactions, and illustrate a partial `multi-dimensional Bethe Ansatz' or `quantum-KAM theorem'. The lattice analogs of these functions exist for N<=L^[d/2] where L is the linear size of the box, and are common eigenstates of Bose-Hubbard Hamiltonians and spin-1/2 XXZ Heisenberg models.

cond-mat.stat-mech↗

arXiv2001

Non-uniform ground state for the Bose gas

We study the ground state, sum a_X |X>, of N hard-core bosons on a finite lattice in configuration space, X={x_1,...,x_N}. All a_X being positive, the ratios a_X / sum a_Y can be interpreted as probabilities P_a (X). Let E denote the energy of the ground state and B_X the number of nearest-neighbor particle-hole pairs in the configuration X. We prove the concentration of P_a to X's with B_X in a sqrt(|E|)-neighborhood of |E|, show that the average of a_X over configurations with B_X=n increases exponentially with n, discuss fluctuations about this average, derive upper and lower bounds on E and give an argument for off-diagonal long-range order in the ground state.

cond-mat.stat-mech↗

arXiv2000

Commensurate and incommensurate correlations in Haldane gap antiferromagnets

We analyze the onset of incommensurabilities around the VBS point of the S=1 bilinear-biquadratic model. We propose a simple effective field theory which is capable of reproducing all known properties of the commensurate-incommensurate transition at the disorder point $θ_{\rm vbs}$. Moreover, the theory predicts another special point $θ_{\rm disp}$, distinct from the VBS point, where the Haldane gap behaves singularly. The ground state energy density is an analytic function of the model parameters everywhere, thus we do not have phase transitions in the conventional sense.

cond-mat.str-el↗

arXiv1999

Ground state of the hard-core Bose gas on lattice I. Energy estimates

We investigate the properties of the ground state of a system of interacting bosons on regular lattices with coordination number $k\geq 2$. The interaction is a pure, infinite, on-site repulsion. Our concern is to give an improved upper bound on the ground state energy per site. For a density $ρ$ a trivial upper bound is known to be $-kρ(1-ρ)$. We obtain a smaller variational bound within a reasonably large family of trial functions. The estimates make use of a large deviation principle for the energy of the Ising model on the same lattice.

cond-mat.stat-mech↗