We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an appropriate time-dependent Schrödinger operator.

A debate has appeared in the literature on loop quantum gravity and spin foams, over whether the secondary simplicity constraints, reducing the connection to be Levi-Civita, should imply the shape matching conditions, reducing twisted geometries to Regge geometries. We address the question using a simple model with a flat dynamics, in which secondary simplicity constraints arise from a dynamical preservation of the primary ones. We find that shape matching conditions arise, thus providing support to an affirmative question. The origin of these extra conditions is to be found in the different graph localisation of the Hamiltonian and primary simplicity constraints. Our results are consistent with previous claims by Dittrich and Ryan, and extend their validity to Lorentzian signature and arbitrary cellular decompositions. We show in particular how the (gauge-invariant version of the) twist angle ξ featuring in twisted geometries equals on-shell the Regge dihedral angle multiplied by the Immirzi parameter, thus recovering the discrete extrinsic geometry from the Ashtekar-Barbero holonomy. Finally, we confirm that flatness implies both the Levi-Civita and the shape-matching conditions using twisted geometries and a 4-dimensional version of the vertex condition appearing in 't Hooft's polygon model.

Under unitary time evolution, expectation values of physically reasonable observables often evolve towards the predictions of equilibrium statistical mechanics. The eigenstate thermalization hypothesis (ETH) states that this is also true already for individual energy eigenstates. Here we aim at elucidating the emergence of the ETH for observables that can realistically be measured due to their high degeneracy, such as local, extensive, or macroscopic observables. We bisect this problem into two parts, a condition on the relative overlaps and one on the relative phases between the eigenbases of the observable and Hamiltonian. We show that the relative overlaps are unbiased for highly degenerate observables and demonstrate that unless relative phases conspire to cumulative effects, this makes such observables verify the ETH. Through this we elucidate potential pathways towards proofs of thermalization.

A crucial point in statistical mechanics is the definition of the notion of thermal equilibrium, which can be given as the state that maximises the von Neumann entropy, under the validity of some constraints. Arguing that such a notion can never be experimentally probed, in this paper we propose a new notion of thermal equilibrium, focused on observables rather than on the full state of the quantum system. We characterise such notion of thermal equilibrium for an arbitrary observable via the maximisation of its Shannon entropy and we bring to light the thermal properties that it heralds. The relation with Gibbs ensembles is studied and understood. We apply such a notion of equilibrium to a closed quantum system and show that there is always a class of observables which exhibits thermal equilibrium properties and we give a recipe to explicitly construct them. Eventually, an intimate connection with the Eigenstate Thermalisation Hypothesis is brought to light.

In this letter we extend the so-called typicality approach, originally formulated in statistical mechanics contexts, to SU(2) invariant spin network states. Our results do not depend on the physical interpretation of the spin-network, however they are mainly motivated by the fact that spin-network states can describe states of quantum geometry, providing a gauge-invariant basis for the kinematical Hilbert space of several background independent approaches to quantum gravity. The first result is, by itself, the existence of a regime in which we show the emergence of a typical state. We interpret this as the prove that, in that regime there are certain (local) properties of quantum geometry which are "universal". Such set of properties is heralded by the typical state, of which we give the explicit form. This is our second result. In the end, we study some interesting properties of the typical state, proving that the area-law for the entropy of a surface must be satisfied at the local level, up to logarithmic corrections which we are able to bound

We report on a search for charged massive resonances decaying to top (t) and bottom (b) quarks in the full data set of proton-antiproton collisions at a center-of-mass energy of root s = 1.96 TeV collected by the CDF II detector at the Tevatron, corresponding to an integrated luminosity of 9.5 fb(-1). No significant excess above the standard model background prediction is observed. We set 95% Bayesian credibility mass-dependent upper limits on the heavy charged-particle production cross section times branching ratio to tb. Using a standard model extension with a W' -> tb and left-right-symmetric couplings as a benchmark model, we constrain the W' mass and couplings in the 300-900 GeV/c(2) range. The limits presented here are the most stringent for a charged resonance with mass in the range 300-600 GeV/c(2) decaying to top and bottom quarks

We exploit the tripartite negativity to study the thermal correlations in a tripartite system, that is the three outer spins interacting with the central one in a spin-star system. We analyze the dependence of such correlations on the homogeneity of the interactions, starting from the case where central-outer spin interactions are identical and then focusing on the case where the three coupling constants are different. We single out some important differences between the negativity and the concurrence.

A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical realization. Conveniently, when working only with the statistical outcomes of projective and positive operator-valued measurements this is not a hindrance. To track ensemble realizations and so remove the shortcoming, we explore geometric quantum states and explain their physical significance. We emphasize two main consequences: one in quantum state manipulation and one in quantum thermodynamics.