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We study the enhancement of tunneling through a potential barrier $V(x)$ by a time-dependent electric field with special emphasis on pulse-shaped vector potentials such as ${A}_{x}(t)={A}_{0}/{cosh}^{2}(\ensuremath{\omega}t)$. In addition to the known effects of preacceleration and potential deformation already present in the adiabatic regime, as well as energy mixing in analogy to the Franz-Keldysh effect in the nonadiabatic (impulse) regime, the pulse ${A}_{x}(t)$ can enhance tunneling by ``pushing'' part of the wave function out of the rear end of the barrier. Aside from the natural applications in condensed matter and atomic physics, these findings could be relevant for nuclear fusion, where pulses ${A}_{x}(t)$ with $\ensuremath{\omega}=1\phantom{\rule{0.28em}{0ex}}\mathrm{keV}$ and peak field strengths of ${10}^{16}\phantom{\rule{0.28em}{0ex}}\mathrm{V}/\mathrm{m}$ might enhance tunneling rates significantly.

Via the hierarchy of correlations, we study the strongly interacting Fermi-Hubbard model in the Mott insulator state and couple it to a Markovian environment that constantly monitors the particle numbers ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{\ensuremath{\mu}}^{\ensuremath{\uparrow}}$ and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{\ensuremath{\mu}}^{\ensuremath{\downarrow}}$ for each lattice site $\ensuremath{\mu}$. As expected, the environment induces an imaginary part $\ensuremath{\gamma}$ (i.e., the decay rate) of the quasiparticle frequencies ${\ensuremath{\omega}}_{\mathbf{k}}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{\mathbf{k}}\ensuremath{-}i\ensuremath{\gamma}$, and it tends to diminish the correlations between lattice sites. Surprisingly, the environment also steers the state of the system on intermediate timescales $O(1/\ensuremath{\gamma})$ to a prerelaxed state very similar to the prethermalized state after a quantum quench (i.e., suddenly switching on the hopping rate $J$). Full relaxation or thermalization occurs via local on-site heating and takes much longer.

Motivated by the recent interest in non-equilibrium phenomena in quantum many-body systems, we study strongly interacting fermions on a lattice by deriving and numerically solving quantum Boltzmann equations that describe their relaxation to thermodynamic equilibrium.The derivation is carried out by inspecting the hierarchy of correlations within the framework of the 1/Z-expansion. Applying the Markov approximation, we obtain the dynamic equations for the distribution functions. Interestingly, we find that in the strong-coupling limit, collisions between particles and holes dominate over particle-particle and hole-hole collisions -- in stark contrast to weakly interacting systems. As a consequence, our numerical simulations show that the relaxation time scales strongly depend on the type of excitations (particles or holes or both) that are initially present., Comment: 15 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1812.08581

We consider deuterium-tritium fusion as a generic example for general fusion reactions. For initial kinetic energies in the keV regime, the reaction rate is exponentially suppressed due to the Coulomb barrier between the nuclei, which is overcome by tunneling. Here, we study whether the tunneling probability could be enhanced by an additional electromagnetic field, such as an x-ray free electron laser (XFEL). We find that the XFEL frequencies and field strengths required for this dynamical assistance mechanism should come within reach of present-day or near-future technology.

Employing time-resolved photoelectron spectroscopy we analyze the relaxation dynamics of hot electrons in the charge density wave / Mott material 1T-TaS_2. At 1.2 eV above the Fermi level we observe a hot electron lifetime of 12 +- 5 fs in the metallic state and of 60 +- 10 fs in the broken symmetry ground state - a direct consequence of the reduced phase space for electron-electron scattering determined by the Mott gap. Boltzmann equation calculations which account for the interaction of hot electrons in a Bloch band with a doublon-holon excitation in the Mott state provide insight into the unoccupied electronic structure in the correlated state., Comment: 6 pages, 3 figures

Via the hierarchy of correlations, we study the Mott insulator phase of the Fermi-Hubbard model in the limit of strong interactions and derive a quantum Boltzmann equation describing its relaxation dynamics. In stark contrast to the weakly interacting case, we find that the scattering cross sections strongly depend on the momenta of the colliding quasi-particles and holes. Therefore, the relaxation towards equilibrium crucially depends on the spectrum of excitations. For example, for particle-hole excitations directly at the minimum of the (direct) Mott gap, the scattering cross sections vanish such that these excitations can have a very long life-time., 18 pages

We study quantum tunneling of a composite object, which has a dipole or quadrupole moment coupled with quantized (photon or gravitational) radiation field, through a {\delta} potential barrier. The dipole or quadrupole moment is represented by an oscillator in the relative coordinate of two constituent particles of the object. The center of mass degrees of freedom of the object is not directly coupled with the radiation field. However, we show that, for the object with the oscillator in the excited state, dissipation caused by the radiation field can suppress its quantum tunneling rate in the center of mass degrees of freedom. In addition, when the initial energy of its center of mass motion is similar to that of the excited state of the oscillator, a spatial superposition state of the object prepared by the barrier can decohere due to the radiation field. The main purpose of this article is to investigate how two different interplays (i) among the center of mass, the relative coordinate degrees of freedom and the potential barrier, and (ii) between the relative coordinate degrees of freedom and the radiation field, can affect the quantum tunneling and the creation of the spatial superposition state of the object. Our toy model can give insight into tests of quantum tunneling and quantum superposition of atoms or molecules with its dipole or quadrupole moment coupled with the radiation field., Comment: 19 pages, 6 figures, version to appear in Class. Quantum Grav

The expansion of the partition function for large coordination number $Z$ is a long standing method and has formerly been used to describe the Ising model at finite temperatures. We extend this approach and study the interacting Bose gas at finite temperatures. An analytical expression for the free energy is derived which is valid for weakly interacting and strongly interacting bosons. The transition line which separates the superfluid phase from Mott insulating/normal gas phase is shown for fillings $\langle\hat n\rangle=1$ and $\langle\hat n\rangle=2$. For unit filling, our findings agree qualitatively with Quantum Monte-Carlo results. Contrary to the well-known mean-field result, the shift of the critical temperature in the weakly interacting regime is apparent., 6 pages, 5 figures (in press in Phys.Rev. A)

Based on a rather general low-energy effective action (interacting quantum fields in classical curved spacetimes), we calculate potential signatures of new physics (e.g., quantum gravity) at ultra-high energies (such as the Planck scale) in the anisotropies of the cosmic microwave background radiation. Special emphasis is laid on the correct treatment of the initial state, which was not derived rigorously in previous works. These Planck-scale interactions create non-Gaussian contributions, and we focus on the three-point function as the most promising observable, which also allows discrimination between models violating and those obeying Lorentz invariance.

We study the optical response of a suspended graphene field-effect transistor in magnetic fields of up to 9 T (quantum Hall regime). With an illumination power of only 3 {\mu}W, we measure a photocurrent of up to 400 nA, corresponding to a photo-responsivity of 0.14 A/W, which we believe to be the highest value ever measured in single-layer graphene. We estimate that every absorbed photon creates more than 8 electron-hole pairs, which demonstrates highly effective carrier multiplication. As suggested by the dependence of the photocurrent on gate voltage and magnetic field, we propose a ballistic two-stage mechanism where the incident photons create primary charge carriers which then excite secondary charge carriers in the chiral edge states via Auger-type inelastic Coulomb scattering processes at the graphene edge., Comment: 11 Pages, 4 Figures

We discuss decrease of coherence in a massive system due to the emission of gravitational waves. In particular we investigate environmental gravitational decoherence in the context of an interference experiment. The time-evolution of the reduced density matrix is solved analytically using the path-integral formalism. Furthermore, we study the impact of a tensor noise onto the coherence properties of massive systems. We discuss that a particular choice of tensor noise shows similarities to a mechanism proposed by Diosi and Penrose., Comment: 8 pages, 2 figures, based on a talk presented by FS at DICE 2014, Castiglioncello, Italy, 15th-19th September 2014

Motivated by realistic scattering processes of composite systems, we study the dynamics of a two-particle bound system which is scattered at a mirror. The physics of the scattering process will be discussed in the cases when only one particle interacts directly with the mirror and when both particles are scattered directly. It is shown that the coherence between the transmitted and the reflected wave-packet becomes reduced due to the scattering process. When both particles interact directly with the mirror, the system exhibits long-lived resonances. The results should be of interest for interference experiments with composite systems., Comment: 5 pages, 11 figures

We study a quantum quench in the Bose-Hubbard model where the tunneling rate $J$ is suddenly switched from zero to a finite value in the Mott regime. In order to solve the many-body quantum dynamics far from equlibrium, we consider the reduced density matrices for a finite number (one, two, three, etc.) of lattice sites and split them up into on-site density operators, i.e., the mean field, plus two-point and three-point correlations etc. Neglecting three-point and higher correlations, we are able to numerically simulate the time-evolution of the few-site density matrices and the two-point quantum correlations (e.g., their effective light-cone structure) for a comparably large number ${\cal O}(10^3)$ of lattice sites.

We study electronic transport in graphene under the influence of a transversal magnetic field B(r)=B(x)ez with the asymptotics B(x→±∞)=±B0, which could be realized via a folded graphene sheet in a constant magnetic field, for example. By solving the effective Dirac equation, we find robust modes with a finite energy gap which propagate along the fold-where particles and holes move in opposite directions. Exciting these particle-hole pairs with incident (optical or infrared) photons would then generate a nearly perfect charge separation and thus a strong magnetophotoelectric or magnetothermoelectric effect-even at room temperature.

We study the Mott phase of the Bose-Hubbard model on a tilted lattice. On the (Gutzwiller) mean-field level, the tilt has no effect -- but quantum fluctuations entail particle-hole pair creation via tunneling. For small potential gradients (long-wavelength limit), we derive a quantitative analogy to the Sauter-Schwinger effect, i.e., electron-positron pair creation out of the vacuum by an electric field. For large tilts, we obtain resonant tunneling related to Bloch oscillations., Comment: 4 pages, 1 figure

We address the issue why a cosmological constant (dark energy) possesses a small positive value instead of being zero. Motivated by the cosmic landscape picture, we mimic the dark energy by a scalar field with potential wells and show that other degrees of freedom interacting with it can localize this field by decoherence in one of the wells. Dark energy can then acquire a small positive value. We also show that the additional degrees of freedom enhance the tunneling rate between the wells. The consideration is performed in detail for the case of two wells and then extended to a large number of wells., Comment: 39 pages, 2 figures, final version

Within a generalized Caldeira-Leggett model we analyze the conditions under which a bosonic heat bath can entangle two microscopic quantum systems at a distance $r$. We find that the attainable entanglement is extremely distance-sensitive. Significant entanglement can only be achieved if the systems are within a {\em microscopic} distance that is of order of the cut-off wavelength $\lambda$ of the system-bath interaction. At larger distances the maximal entanglement is exponentially suppressed with a decay length of order $\lambda$. We conclude that entanglement generation via a heat bath is not suitable for entangling remote objects., Comment: 4 pages, 3 figures, new title, final version to appear in Phys. Rev. Lett

In many condensed-matter systems, it is very useful to introduce a quasi-particle approach, which is based on some sort of linearization around a suitable background state. In order to be a systematic and controlled approximation, this linearization should be justified by an expansion into the powers of some small control parameter. Here, we present a method for general lattice Hamiltonians with large coordination numbers Z 1, which is based on an expansion into the powers of 1/Z. In order to demonstrate the generality of our method, we apply it to various spin systems, as well as the Bose and Fermi–Hubbard model.

For a general O(N) model, we study the time-dependent phase transition from a state with broken symmetry ≠ 0 to the symmetric phase = 0. During this non-equilibrium process, the primordial quantum (or thermal) fluctuations of the initial Goldstone modes are frozen and result in a deviation from the final ground (or thermal) state. For very slow transitions, we find that these fluctuations display a universal scaling behaviour. Their spectra are universal functions of a single parameter, which combines the initial frequency of the Goldstone modes and the sweep rate. As a result, the final two-point function [φa(r)φb(r')] is not exponentially suppressed at large distances Δr = r - r' (as it would be in the ground state) but decays polynomially in 1/|Δr|. Finally, we exemplify this universal behaviour for the transition from the super-fluid phase to the Mott state in the Bose-Hubbard model.