Non-Gibbs states on a Bose-Hubbard lattice

We study the equilibrium properties of the repulsive quantum Bose-Hubbard model at high temperatures in arbitrary dimensions, with and without disorder. In its microcanonical setting the model conserves energy and particle number. The microcanonical dynamics is characterized by a pair of two densities: energy density $\varepsilon$ and particle number density $n$. The macrocanonical Gibbs distribution also depends on two parameters: the inverse nonnegative temperature $\beta$ and the chemical potential $\mu$. We prove the existence of non-Gibbs states, that is, pairs $(\varepsilon,n)$ which cannot be mapped onto $(\beta,\mu)$. The separation line in the density control parameter space between Gibbs and non-Gibbs states $\varepsilon \sim n^2$ corresponds to infinite temperature $\beta=0$. The non-Gibbs phase cannot be cured into a Gibbs one within the standard Gibbs formalism using negative temperatures.Comment: 8 pages, 1 figure, misprints correcte

Periodic Mean-Field Solutions and the Spectra of Discrete Bosonic Fields: Trace Formula for Bose-Hubbard Models

We consider the many-body spectra of interacting bosonic quantum fields on a lattice in the semiclassical limit of large particle number $N$. We show that the many-body density of states can be expressed as a coherent sum over oscillating long-wavelength contributions given by periodic, non-perturbative solutions of the, typically non-linear, wave equation of the classical (mean-field) limit. To this end we construct the semiclassical approximation for both the smooth and oscillatory part of the many-body density of states in terms of a trace formula starting from the exact path integral form of the propagator between many-body quadrature states. We therefore avoid the use of a complexified classical limit characteristic of the coherent state representation. While quantum effects like vacuum fluctuations and gauge invariance are exactly accounted for, our semiclassical approach captures quantum interference and therefore is valid well beyond the Ehrenfest time where naive quantum-classical correspondence breaks down. Remarkably, due to a special feature of harmonic systems with incommesurable frequencies, our formulas are generically valid also in the free-field case of non-interacting bosons.Comment: submitted to Phys. Rev.

The semiclassical propagator in fermionic Fock space

We present a rigorous derivation of a semiclassical propagator for anticommuting (fermionic) degrees of freedom, starting from an exact representation in terms of Grassmann variables. As a key feature of our approach the anticommuting variables are integrated out exactly, and an exact path integral representation of the fermionic propagator in terms of commuting variables is constructed. Since our approach is not based on auxiliary (Hubbard-Stratonovich) fields, it surpasses the calculation of fermionic determinants yielding a standard form $\int {\cal D}[\psi,\psi^{*}] {\rm e}^{i R[\psi,\psi^{*}]}$ with real actions for the propagator. These two features allow us to provide a rigorous definition of the classical limit of interacting fermionic fields and therefore to achieve the long-standing goal of a theoretically sound construction of a semiclassical van Vleck-Gutzwiller propagator in fermionic Fock space. As an application, we use our propagator to investigate how the different universality classes (orthogonal, unitary and symplectic) affect generic many-body interference effects in the transition probabilities between Fock states of interacting fermionic systems.Comment: 20 pages, 1 figur

Many-Body Spin Echo

We predict a universal echo phenomenon present in the time evolution of many-body states of interacting quantum systems described by Fermi-Hubbard models. It consists of the coherent revival of transition probabilities echoing a sudden flip of the spins that, contrary to its single-particle (Hahn) version, is not dephased by interactions or spin-orbit coupling. The many-body spin echo signal has a universal shape independent of the interaction strength, and an amplitude and sign depending only on combinatorial relations between the number of particles and the number of applied spin flips. Our analytical predictions, based on semiclassical interfering amplitudes in Fock space associated with chaotic mean-field solutions, are tested against extensive numerical simulations confirming that the coherent origin of the echo lies in the existence of anti-unitary symmetries.Comment: 5 pages, 4 figure

Aspects of integrability in a classical model for non-interacting fermionic fields

In this work we investigate the issue of integrability in a classical model for noninteracting fermionic fields. This model is constructed via classical-quantum correspondence obtained from the semiclassical treatment of the quantum system. Our main finding is that the classical system, contrary to the quantum system, is not integrablein general. Regarding this contrast it is clear that in general classical models for fermionic quantum systems have to be handled with care. Further numerical investigation of the system showed that there may be islands of stability in the phase space. We also investigated a similar model that is used in theoretical chemistry and found this one to be most probably integrable, although also here the integrability is not assured by the quantum-classical correspondence principle

Conductance and Thermopower of Ballistic Andreev Cavities

When coupling a superconductor to a normal conducting region the physical properties of the system are highly affected by the superconductor. We will investigate the effect of one or two superconductors on the conductance of a ballistic chaotic quantum dot to leading order in the total channel number using trajectory based semiclassics. The results show that the effect of one superconductor on the conductance is of the order of the number of channels and that the sign of the correction from the Drude conductance depends on the particular ratios of the numbers of channels of the superconducting and normal conducting leads. In the case of two superconductors with the same chemical potential we will also see how the conductance and the sign of quantum corrections are affected by their phase difference. As far as random matrix theory results exist these are reproduced by our calculations. Furthermore in the case that the chemical potential of the superconductors is the same as that of one of the two normal leads the conductance shows, under certain conditions, similar effects as a normal metal-superconductor junction. The semiclassical framework is also able to treat the thermopower of chaotic Andreev billiards consisting of one chaotic dot, two normal leads and two superconducting islands and shows it to be antisymmetric in the phase difference of the superconductors.Comment: 23 page

ATLAS monitored drift tube chambers for super-LHC

After the high-luminosity upgrade of the Large Hadron Collider (LHC) at CERN, the ATLAS muon spectrometer is expected to work at 10 times increased background rates of gammas and neutrons. This is challenging as the momentum resolution of the spectrometer is expected to be 10 %. This requires a single tube resolution of the muon drift tubes of 80 mum. At background rates around 1000 Hz/cm2 space charge effects will lead in the slow and non-linear AR:CO2 = 93:7 gas mixture to a degradation of the drift-tube spatial resolution. This was studied before experimentally for gammas and low energetic neutrons. Almost no information exists for fast neutrons. Therefore, we organized our studies under the following aspects: - We investigated the influence of 11 MeV neutrons on the position resolution of ATLAS MDT chambers. At flux densities between 4 and 16 kHz/cm2, almost no influence on the position resolution was found, it degrades by only 10 mum at a detection efficiency of only 4*10-4. - We investigated inert gas mixtures on fastness and linearity of their position-drifttime (r-t) relation. At a reduction of the maximum drift time by a factor of 2, the use of the present hardware and electronics might be possible. For our experimental studies we used our Munich cosmic ray facility. Two gas mixtures show almost identical position resolution as the standard gas. - For spectrometer regions of highest background rates we contributed to the investigation of newly developed 15 mm drift tubes. Position resolutions have been measured as a function of gamma background rates between 0 and 1400 Hz/cm2. - Garfield simulations have been performed to simulate space charge effects due to gamma irradiation. Results will be presented for the standard geometry as well as for the new 15 mm drift tubes.Comment: 3 pages, 7 figures, conferenc

The density of states of chaotic Andreev billiards

Quantum cavities or dots have markedly different properties depending on whether their classical counterparts are chaotic or not. Connecting a superconductor to such a cavity leads to notable proximity effects, particularly the appearance, predicted by random matrix theory, of a hard gap in the excitation spectrum of quantum chaotic systems. Andreev billiards are interesting examples of such structures built with superconductors connected to a ballistic normal metal billiard since each time an electron hits the superconducting part it is retroreflected as a hole (and vice-versa). Using a semiclassical framework for systems with chaotic dynamics, we show how this reflection, along with the interference due to subtle correlations between the classical paths of electrons and holes inside the system, are ultimately responsible for the gap formation. The treatment can be extended to include the effects of a symmetry breaking magnetic field in the normal part of the billiard or an Andreev billiard connected to two phase shifted superconductors. Therefore we are able to see how these effects can remold and eventually suppress the gap. Furthermore the semiclassical framework is able to cover the effect of a finite Ehrenfest time which also causes the gap to shrink. However for intermediate values this leads to the appearance of a second hard gap - a clear signature of the Ehrenfest time.Comment: Refereed version. 23 pages, 19 figure

Numerical Analysis of the Non-uniform Sampling Problem

We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays a key role in the numerical solution of the non-uniform sampling problem. In the one approach (often proposed in the literature) the finite-dimensional model leads to an ill-posed problem even in very simple situations. The other approach that we consider leads to a well-posed problem that preserves important structural properties of the original infinite-dimensional problem and gives rise to efficient numerical algorithms. Furthermore a fast multilevel algorithm is presented that can reconstruct signals of unknown bandwidth from noisy non-uniformly spaced samples. We also discuss the design of efficient regularization methods for ill-conditioned reconstruction problems. Numerical examples from spectroscopy and exploration geophysics demonstrate the performance of the proposed methods