arXiv subjects

A. Pelster

Publications and source records attributed to A. Pelster.

At least 19 recordsLinked to original sources

arXiv2021

Bosonic continuum theory of one-dimensional lattice anyons

Anyons with arbitrary exchange phases exist on 1D lattices in ultracold gases. Yet, known continuum theories in 1D do not match. We derive the continuum limit of 1D lattice anyons via interacting bosons. The theory maintains the exchange phase periodicity fully analogous to 2D anyons. This provides a mapping between experiments, lattice anyons, and continuum theories, including Kundu anyons with a natural regularization as a special case. We numerically estimate the Luttinger parameter as a function of the exchange angle to characterize long-range signatures of the theory and predict different velocities for left- and right-moving collective excitations.

cond-mat.quant-gas↗

arXiv2018

Improving Mean-Field Theory for Bosons in Optical Lattices via Degenerate Perturbation Theory

The objective of this paper is the theoretical description of the Mott-insulator to superfluid quantum phase transition of a Bose gas in an optical lattice. In former works the Rayleigh-Schrödinger perturbation theory was used within a mean-field approach, which yields partially non-physical results since the degeneracy between two adjacent Mott lobes is not taken into account. In order to correct such non-physical results we apply the Brillouin-Wigner perturbation theory to the mean-field approximation of the Bose-Hubbard model. Detailed explanations of how to use the Brillouin-Wigner theory are presented, including a graphical approach that allows to efficiently keep track of the respective analytic terms. To prove the validity of this computation, the results are compared with other works. Besides the analytic calculation of the phase boundary from Mott-insulator to superfluid phase, the condensate density is also determined by simultaneously solving two algebraic equations. The analytical and numerical results turn out to be physically meaningful and can cover a region of system parameters inaccessible until now. Our results are of particular interest provided an harmonic trap is added to the former calculations in an homogeneous system, in view of describing an experiment within the local density approximation. Thus, the paper represents an essential preparatory work for determining the experimentally observed wedding-cake structure of particle-density profile at both finite temperature and hopping.

cond-mat.quant-gas↗

arXiv2017

Low-Lying Excitation Modes of Trapped Dipolar Fermi Gases: From Collisionless to Hydrodynamic Regime

By means of the Boltzmann-Vlasov kinetic equation we investigate dynamical properties of a trapped, one-component Fermi gas at zero temperature, featuring the anisotropic and long-range dipole-dipole interaction. To this end, we determine an approximate solution by rescaling both space and momentum variables of the equilibrium distribution, thereby obtaining coupled ordinary differential equations for the corresponding scaling parameters. Based on previous results on how the Fermi sphere is deformed in the hydrodynamic regime of a dipolar Fermi gas, we are able to implement the relaxation-time approximation for the collision integral. Then, we proceed by linearizing the equations of motion around the equilibrium in order to study both the frequencies and the damping of the low-lying excitation modes all the way from the collisionless to the hydrodynamic regime. Our theoretical results are expected to be relevant for understanding current experiments with trapped dipolar Fermi gases.

cond-mat.quant-gas↗

arXiv2017

Driven Bose-Hubbard Model with a Parametrically Modulated Harmonic Trap

We investigate a one-dimensional Bose-Hubbard model in a parametrically driven global harmonic trap. The delicate interplay of both the local atom interaction and the global driving allows to control the dynamical stability of the trapped quantum many-body state. The mechanism is illustrated for weak interaction by a discretized Gross-Pitaevskii equation within a Gaussian variational ansatz, yielding to a Mathieu equation for the condensate width. The parametric resonance condition can be tuned by the atom interaction strength. For stronger interaction, this mechanism is confirmed by results of the numerically exact time-evolving block decimation scheme. The global modulation also induces an effective time-independent inhomogeneous hopping strength for the atoms.

cond-mat.quant-gas↗

arXiv2010

Excitation Spectra of Bosons in Optical Lattices from Schwinger-Keldysh Calculation

Within the Schwinger-Keldysh formalism we derive a Ginzburg-Landau theory for the Bose-Hubbard model which describes the real-time dynamics of the complex order parameter field. Analyzing the excitations in the vicinity of the quantum phase transition it turns out that particle/hole dispersions in the Mott phase map continuously onto corresponding amplitude/phase excitations in the superfluid phase, which have been detected recently by Bragg spectroscopy measurements.

cond-mat.quant-gas↗

arXiv2010

Real-Time Ginzburg-Landau Theory for Bosons in Optical Lattices

Within the Schwinger-Keldysh formalism we derive a Ginzburg-Landau theory for the Bose-Hubbard model which describes the real-time dynamics of the complex order parameter field. Analyzing the excitations in the vicinity of the quantum phase transitions it turns out that particle/hole dispersions in the Mott phase map continuously onto corresponding amplitude/phase excitations in the superfluid phase. Furthermore, in the superfluid phase we find a sound mode, which is in accordance with recent Bragg spectroscopy measurements in the Bogoliubov regime, as well as an additional gapped mode, which seems to have been detected via lattice modulation.

cond-mat.quant-gas↗

arXiv2009

Quantum Phase Diagram of Bosons in Optical Lattices

We work out two different analytical methods for calculating the boundary of the Mott-insulator-superfluid (MI-SF) quantum phase transition for scalar bosons in cubic optical lattices of arbitrary dimension at zero temperature which improve upon the seminal mean-field result. The first one is a variational method, which is inspired by variational perturbation theory, whereas the second one is based on the field-theoretic concept of effective potential. Within both analytical approaches we achieve a considerable improvement of the location of the MI-SF quantum phase transition for the first Mott lobe in excellent agreement with recent numerical results from Quantum Monte-Carlo simulations in two and three dimensions. Thus, our analytical results for the whole quantum phase diagram can be regarded as being essentially exact for all practical purposes.

cond-mat.stat-mech↗

arXiv2007

Collective Oscillations in Trapped Bose-Einstein Condensed Gases in the Presence of Weak Disorder

The influence of a weak random potential on the collective modes of a trapped interacting Bose-Einstein condensate at zero temperature is calculated in the limit when the correlation length of the disorder is smaller than the healing length of the superfluid. The problem is solved in the Thomas-Fermi limit by generalizing the superfluid hydrodynamic equations to allow for the presence of weak disorder. We find that the disorder-induced frequency-shifts of the low-energy excitations can be of the same order of magnitude as the beyond mean-field corrections in the normal interaction recently observed experimentally.

cond-mat.other↗

arXiv2007

Thermodynamics of a Bose-Einstein Condensate with Weak Disorder

We consider the thermodynamics of a homogeneous superfluid dilute Bose gas in the presence of weak quenched disorder. Following the zero-temperature approach of Huang and Meng, we diagonalize the Hamiltonian of a dilute Bose gas in an external random delta-correlated potential by means of a Bogoliubov transformation. We extend this approach to finite temperature by combining the Popov and the many-body T-matrix approximations. This approach permits us to include the quasi-particle interactions within this temperature range. We derive the disorder-induced shifts of the Bose-Einstein critical temperature and of the temperature for the onset of superfluidity by approaching the transition points from below, i.e., from the superfluid phase. Our results lead to a phase diagram consistent with that of the finite-temperature theory of Lopatin and Vinokur which was based on the replica method, and in which the transition points were approached from above.

cond-mat.other↗

arXiv2006

Self-Organized Formation of Retinotopic Projections Between Manifolds of Different Geometries -- Part 3: Spherical Geometries

We follow our general model in Ref. [3] and analyze the formation of retinotopic projections for the biologically relevant situation of spherical geometries. To this end we elaborate both a linear and a nonlinear synergetic analysis which results in order parameter equations for the dynamics of connection weights between two spherical cell sheets. We show that these equations of evolution provide stable stationary solutions which correspond to retinotopic modes. A further analysis of higher modes furnishes proof that our model describes the emergence of a perfect one-to-one retinotopy between two spheres.

physics.bio-ph↗

arXiv2006

Mean-field phase diagram of disordered bosons in a lattice at non-zero temperature

Bosons in a periodic lattice with on-site disorder at low but non-zero temperature are considered within a mean-field theory. The criteria used for the definition of the superfluid, Mott insulator and Bose glass are analysed. Since the compressibility does never vanish at non-zero temperature, it can not be used as a general criterium. We show that the phases are unambiguously distinguished by the superfluid density and the density of states of the low-energy exitations. The phase diagram of the system is calculated. It is shown that even a tiny temperature leads to a significant shift of the boundary between the Bose glass and superfluid.

cond-mat.other↗

arXiv2004

Reentrant Phenomenon in Quantum Phase Diagram of Optical Boson Lattice

We calculate the location of the quantum phase transitions of a bose gas trapped in an optical lattice as a function of effective scattering length $a_{\eff}$ and temperature $T$. Knowledge of recent high-loop results on the shift of the critical temperature at weak couplings is used to locate a {\em nose} in the phase diagram above the free Bose-Einstein critical temperature $T_c^{(0)}$, thus predicting the existence of a reentrant transition {\em above} $T_c^{(0)}$, where a condensate should form when {\em increasing} $a_{\eff}$. At zero temperature, the transition to the normal phase produces the experimentally observed Mott insulator.

cond-mat.stat-mech↗

arXiv2000

Functional Differential Equations for the Free Energy and the Effective Energy in the Broken-Symmetry Phase of phi^4-Theory and Their Recursive Graphical Solution

Extending recent work on QED and the symmetric phase of the euclidean multicomponent scalar ϕ^4-theory, we construct the vacuum diagrams of the free energy and the effective energy in the ordered phase of ϕ^4-theory. By regarding them as functionals of the free correlation function and the interaction vertices, we graphically solve nonlinear functional differential equations, obtaining loop by loop all connected and one-particle irreducible vacuum diagrams with their proper weights.

hep-th↗

arXiv2000

Variational Approach to Hydrogen Atom in Uniform Magnetic Field of Arbitrary Strength

Extending the Feynman-Kleinert variational approach, we calculate the temperature-dependent effective classical potential governing the quantum statistics of a hydrogen atom in a uniform magnetic at all temperatures. The zero-temperature limit yields the binding energy of the electron which is quite accurate for all magnetic field strengths and exhibits, in particular, the correct logarithmic growth at large fields.

quant-ph↗

arXiv1999

Recursive Graphical Construction for Feynman Diagrams of Quantum Electrodynamics

We present a method for a recursive graphical construction of Feynman diagrams with their correct multiplicities in quantum electrodynamics. The method is first applied to find all diagrams contributing to the vacuum energy from which all n-point functions are derived by functional differentiation with respect to electron and photon propagators, and to the interaction. Basis for our construction is a functional differential equation obeyed by the vacuum energy when considered as a functional of the free propagators and the interaction. Our method does not employ external sources in contrast to traditional approaches.

hep-th↗

arXiv1999

Autoparallels From a New Action Principle

We present a simpler and more powerful version of the recently-discovered action principle for the motion of a spinless point particle in spacetimes with curvature and torsion. The surprising feature of the new principle is that an action involving only the metric can produce an equation of motion with a torsion force, thus changing geodesics to autoparallels. This additional torsion force arises from a noncommutativity of variations with parameter derivatives of the paths due to the closure failure of parallelograms in the presence of torsion

gr-qc↗

arXiv1999

Strong-Coupling Calculation of Fluctuation Pressure of a Membrane Between Walls

We calculate analytically the proportionality constant in the pressure law of a membrane between parallel walls from the strong-coupling limit of variational perturbation theory up to third order. Extrapolating the zeroth to third approximations to infinity yields the pressure constant alpha=0.0797149. This result lies well within the error bounds of the most accurate available Monte-Carlo result 0.0798 +- 0.0003.

cond-mat↗

arXiv1998

Variational Perturbation Theory for Density Matrices

We develop convergent variational perturbation theory for quantum statistical density matrices. The theory is applicable to polynomial as well as nonpolynomial interactions. Illustrating the power of the theory, we calculate the temperature-dependent density of a particle in a double-well and of the electron in a hydrogen atom.

quant-ph↗