arXiv subjects

Andrea Trombettoni

Publications and source records attributed to Andrea Trombettoni.

125 records · Page 7Linked to original sources

arXiv2013

Tunneling of polarized fermions in 3D double wells

We study the tunneling of a spin polarized Fermi gas in a three-dimensional double well potential, focusing on the time dynamics starting from an initial state in which there is an imbalance in the number of particles in the two wells. Although fermions in different doublets of the double well tunnel with different frequencies, we point out that (incoherent) oscillations of a large number of particles can arise, as a consequence of the presence of transverse degrees of freedom. Estimates of the doublet structure and of the occupation of transverse eigenstates for a realistic experimental setup are provided.

cond-mat.quant-gas↗

arXiv2013

Anisotropic Ginzburg-Landau and Lawrence-Doniach Models for Layered Ultracold Fermi Gases

We study the anisotropic Ginzburg-Landau and Lawrence-Doniach models describing a layered superfluid ultracold Fermi gas in optical lattices. We derive the coefficients of the anisotropic Ginzburg-Landau and the mass tensor as a function of anisotropy, filling and interaction, showing that near the unitary limit the effective anisotropy of the masses is significantly reduced. The anisotropy parameter is shown to vary in realistic setups in a wide range of values. We also derive the Lawrence-Doniach model - often used to describe the 2D-3D dimensional crossover in layered superconductors - for a layered ultracold Fermi gas, obtaining a relation between the interlayer Josephson couplings and the Ginzburg-Landau masses. Comparing to the Ginzburg-Landau description, we find that the region of validity of the Lawrence-Doniach model is near the unitary limit.

cond-mat.quant-gas↗

arXiv2013

Statistical Mechanics of an Ideal Gas of Non-Abelian Anyons

We study the thermodynamical properties of an ideal gas of non-Abelian Chern-Simons particles and we compute the second virial coefficient, considering the effect of general soft-core boundary conditions for the two-body wavefunction at zero distance. The behaviour of the second virial coefficient is studied as a function of the Chern-Simons coupling, the isospin quantum number and the hard-coreness parameters. Expressions for the main thermodynamical quantities at the lower order of the virial expansion are also obtained: we find that at this order the relation between the internal energy and the pressure is the same found (exactly) for 2D Bose and Fermi ideal gases. A discussion of the comparison of obtained findings with available results in literature for systems of hard-core non-Abelian Chern-Simons particles is also supplied.

hep-th↗

arXiv2013

Modulational instabilities in lattices with power-law hoppings and interactions

We study the occurrence of modulational instabilities in lattices with non-local, power-law hoppings and interactions. Choosing as a case study the discrete nonlinear Schrödinger equation, we consider one-dimensional chains with power-law decaying interactions (with exponent α) and hoppings (with exponent β): An extensive energy is obtained for α, β>1. We show that the effect of power-law interactions is that of shifting the onset of the modulational instabilities region for α>1. At a critical value of the interaction strength, the modulational stable region shrinks to zero. Similar results are found for effectively short-range nonlocal hoppings (β> 2): At variance, for longer-ranged hoppings (1 < β< 2) there is no longer any modulational stability. The hopping instability arises for q = 0 perturbations, thus the system is most sensitive to the perturbations of the order of the system's size. We also discuss the stability regions in the presence of the interplay between competing interactions - (e.g., attractive local and repulsive nonlocal interactions). We find that noncompeting nonlocal interactions give rise to a modulational instability emerging for a perturbing wave vector q = πwhile competing nonlocal interactions may induce a modulational instability for a perturbing wave vector 0 < q < π. Since for α> 1 and β> 2 the effects are similar to the effect produced on the stability phase diagram by finite range interactions and/or hoppings, we conclude that the modulational instability is "genuinely" long-ranged for 1 < β< 2 nonlocal hoppings.

nlin.PS↗

arXiv2013

Quantum spins on star graphs and the Kondo model

We study the XX model for quantum spins on the star graph with three legs (i.e., on a Y-junction). By performing a Jordan-Wigner transformation supplemented by the introduction of an auxiliary space we find a Kondo Hamiltonian of fermions, in the spin 1 representation of su(2), locally coupled with a magnetic impurity. In the continuum limit our model is shown to be equivalent to the 4-channel Kondo model coupling spin-1/2 fermions with a spin-1/2 impurity and exhibiting a non-Fermi liquid behavior. We also show that it is possible to find a XY model such that - after the Jordan-Wigner transformation - one obtains a quadratic fermionic Hamiltonian directly diagonalizable.

math-ph↗

arXiv2013

XXZ spin-1/2 representation of a finite-U Bose-Hubbard chain at half-integer filling

Using a similarity Hamiltonian renormalization procedure, we determine an effective spin-1/2 representation of the Bose-Hubbard model at half-integer filling and at a finite on-site interaction energy U. By means of bosonization, we are able to recast the effective Hamiltonian as that of a spin-1/2 XXZ magnetic chain with pertinently renormalized coupling and anisotropy parameters. We use this mapping to provide analytical estimates of the correlation functions of the Bose-Hubbard model. We then compare such results with those based on DMRG numerical simulations of the Bose-Hubbard model for various values of U and for a number L of lattice sites as low as L ~ 30. We find an excellent agreement up to 10% between the output of analytical and numerical computations, even for relatively small values of U. Our analysis implies that, also at finite U, the 1D Bose-Hubbard model with suitably chosen parameters may be seen as a quantum simulator of the XXZ chain.

cond-mat.str-el↗

arXiv2012

Statistical Interparticle Potential of an Ideal Gas of Non-Abelian Anyons

We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern-Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of Abelian anyons. In the Abelian case, the statistical potential depends on the statistical parameter and it has a "quasi-bosonic" behaviour for statistical parameter in the range (0,1/2) (non-monotonic with a minimum) and a "quasi-fermionic" behaviour for statistical parameter in the range (1/2,1) (monotonically decreasing without a minimum). In the non-Abelian case the behavior of the statistical potential depends on the Chern- Simons coupling and the isospin quantum number: as a function of these two parameters, a phase diagram with quasi-bosonic, quasi-fermionic and bosonic-like regions is obtained and investigated. Finally, using the obtained expression for the statistical potential, we compute the second virial coefficient of the NACS gas, which correctly reproduces the results available in literature.

cond-mat.quant-gas↗

arXiv2011

Inverse Ising problem for one-dimensional chains with arbitrary finite-range couplings

We study Ising chains with arbitrary multispin finite-range couplings, providing an explicit solution of the associated inverse Ising problem, i.e. the problem of inferring the values of the coupling constants from the correlation functions. As an application, we reconstruct the couplings of chain Ising Hamiltonians having exponential or power-law two-spin plus three- or four-spin couplings. The generalization of the method to ladders and to Ising systems where a mean-field interaction is added to general finite-range couplings is as well as discussed.

cond-mat.stat-mech↗

arXiv2011

Vortex Lines Distribution in Inhomogeneous Lattices

We study the distribution of vortex lines in a three-dimensional lattice with inhomogeneous couplings. We investigate the spatial distribution of the number of vortex lines, showing how the vortex lines are expelled from the region with higher couplings. Results for the correlation functions are presented, together with a discussion of the implications of the obtained results for the vortex distribution in ultracold trapped gases and in neutron stars.

cond-mat.stat-mech↗

arXiv2011

Ultracold atoms in U(2) non-Abelian gauge potentials preserving the Landau levels

We study ultracold atoms subjected to U(2) non-Abelian potentials: we consider gauge potentials having, in the Abelian limit, degenerate Landau levels and we then investigate the effect of general homogeneous non-Abelian terms. The conditions under which the structure of degenerate Landau levels is preserved are classified and discussed. The typical gauge potentials preserving the Landau levels are characterized by a fictitious magnetic field and by an effective spin-orbit interaction, e.g. obtained through the rotation of two-dimensional atomic gases coupled with a tripod scheme. The single-particle energy spectrum can be exactly determined for a class of gauge potentials, whose physical implementation is explicitly discussed. The corresponding Landau levels are deformed by the non-Abelian contribution of the potential and their spin degeneracy is split. The related deformed quantum Hall states for fermions and bosons (in the presence of strong intra-species interaction) are determined far from and at the degeneracy points of the Landau levels. A discussion of the effect of the angular momentum is presented, as well as results for U(3) gauge potentials.

cond-mat.quant-gas↗

arXiv2010

Non-abelian anyons from degenerate Landau levels of ultracold atoms in artificial gauge potentials

We show that non-abelian potentials acting on ultracold gases with two hyperfine levels can give rise to ground states with non-abelian excitations. We consider a realistic gauge potential for which the Landau levels can be exactly determined: the non-abelian part of the vector potential makes the Landau levels non-degenerate. In the presence of strong repulsive interactions, deformed Laughlin ground states occur in general. However, at the degeneracy points of the Landau levels, non-abelian quantum Hall states appear: these ground states, including deformed Moore-Read states (characterized by Ising anyons as quasi-holes), are studied for both fermionic and bosonic gases.

cond-mat.quant-gas↗

arXiv2010

Relativistic Bose-Einstein Condensates: a new system for analogue models of gravity

In this paper we propose to apply the analogy between gravity and condensed matter physics to relativistic Bose-Einstein condensates (RBECs), i.e. condensates composed by relativistic constituents. While such systems are not yet a subject of experimental realization, they do provide us with a very rich analogue model of gravity, characterized by several novel features with respect to their non-relativistic counterpart. Relativistic condensates exhibit two (rather than one) quasi-particle excitations, a massless and a massive one, the latter disappearing in the non-relativistic limit. We show that the metric associated with the massless mode is a generalization of the usual acoustic geometry allowing also for non-conformally flat spatial sections. This is relevant, as it implies that these systems can allow the simulation of a wider variety of geometries. Finally, while in non-RBECs the transition is from Lorentzian to Galilean relativity, these systems represent an emergent gravity toy model where Lorentz symmetry is present (albeit with different limit speeds) at both low and high energies. Hence they could be used as a test field for better understanding the phenomenological implications of such a milder form of Lorentz violation at intermediate energies.

gr-qc↗

arXiv2010

Dipole Oscillations in Fermionic Mixtures

We study dipole oscillations in a general fermionic mixture: starting from the Boltzmann equation, we classify the different solutions in the parameter space through the number of real eigenvalues of the small oscillations matrix. We discuss how this number can be computed using the Sturm algorithm and its relation with the properties of the Laplace transform of the experimental quantities. After considering two components in harmonic potentials having different trapping frequencies, we study dipole oscillations in three-component mixtures. Explicit computations are done for realistic experimental setups using the classical Boltzmann equation without intra-species interactions. A brief discussion of the application of this classification to general collective oscillations is also presented.

cond-mat.quant-gas↗

arXiv2010

Characterization of the Bose-glass phase in low-dimensional lattices

We study by numerical simulation a disordered Bose-Hubbard model in low-dimensional lattices. We show that a proper characterization of the phase diagram on finite disordered clusters requires the knowledge of probability distributions of physical quantities rather than their averages. This holds in particular for determining the stability region of the Bose-glass phase, the compressible but not superfluid phase that exists whenever disorder is present. This result suggests that a similar statistical analysis should be performed also to interpret experiments on cold gases trapped in disordered lattices, limited as they are to finite sizes.

cond-mat.str-el↗

arXiv2009

Effect of random on-site energies on the critical temperature of a lattice Bose gas

We study the effect of random on-site energies on the critical temperature of a non-interacting Bose gas on a lattice. In our derivation the on-site energies are distributed according a Gaussian probability distribution function having vanishing average and variance $v_o^2$. By using the replicated action obtained by averaging on the disorder, we perform a perturbative expansion for the Green functions of the disordered system. We evaluate the shift of the chemical potential induced by the disorder and we compute, for $v_o^2 << 1$, the critical temperature for condensation. We find that, for large filling, disorder slightly enhances the critical temperature for condensation.

cond-mat.stat-mech↗

arXiv2003

Nonlinear Tight-Binding Approximation for Bose-Einstein Condensates in a Lattice

The dynamics of Bose-Einstein condensates trapped in a deep optical lattice is governed by a discrete nonlinear equation (DNL). Its degree of nonlinearity and the intersite hopping rates are retrieved from a nonlinear tight-binding approximation taking into account the effective dimensionality of each condensate. We derive analytically the Bloch and the Bogoliubov excitation spectra, and the velocity of sound waves emitted by a traveling condensate. Within a Lagrangian formalism, we obtain Newtonian-like equations of motion of localized wavepackets. We calculate the ground-state atomic distribution in the presence of an harmonic confining potential, and the frequencies of small amplitude dipole and quadrupole oscillations. We finally quantize the DNL, recovering an extended Bose-Hubbard model.

cond-mat↗

arXiv2003

An O(N) symmetric extension of the Sine-Gordon Equation

We discuss an O(N) exension of the Sine-Gordon (S-G)equation which allows us to perform an expansion around the leading order in large-N result using Path-Integral methods. In leading order we show our methods agree with the results of a variational calculation at large-N. We discuss the striking differences for a non-polynomial interaction between the form for the effective potential in the Gaussian approximation that one obtains at large-N when compared to the N=1 case. This is in contrast to the case when the classical potential is a polynomial in the field and no such drastic differences occur. We find for our large-N extension of the Sine-Gordon model that the unbroken ground state is unstable as one increases the coupling constant (as it is for the original S-G equation) and we determine the stability criteria.

hep-th↗