Unitary equilibrations: probability distribution of the Loschmidt echo

Closed quantum systems evolve unitarily and therefore cannot converge in a strong sense to an equilibrium state starting out from a generic pure state. Nevertheless for large system size one observes temporal typicality. Namely, for the overwhelming majority of the time instants, the statistics of observables is practically indistinguishable from an effective equilibrium one. In this paper we consider the Loschmidt echo (LE) to study this sort of unitary equilibration after a quench. We draw several conclusions on general grounds and on the basis of an exactly-solvable example of a quasi-free system. In particular we focus on the whole probability distribution of observing a given value of the LE after waiting a long time. Depending on the interplay between the initial state and the quench Hamiltonian, we find different regimes reflecting different equilibration dynamics. When the perturbation is small and the system is away from criticality the probability distribution is Gaussian. However close to criticality the distribution function approaches a double peaked, "batman-hood" shaped, universal form.Comment: 15 pages, 16 figure

Cosmic ray production in modified gravity

This paper is a reply to the criticism of our work on particle production in modified gravity by D. Gorbunov and A. Tokareva. We show that their arguments against efficient particle production are invalid. $F(R)$ theories can lead to an efficient generation of high energy cosmic rays in contracting systems.Comment: In response to criticism by referees several clarifying comments are added. The results of the paper remain largely unchanged. Version to appear on EPJ

Conformal Truncation of Chern-Simons Theory at Large NfN_f

We set up and analyze the lightcone Hamiltonian for an abelian Chern-Simons field coupled to $N_f$ fermions in the limit of large $N_f$ using conformal truncation, i.e. with a truncated space of states corresponding to primary operators with dimension below a maximum cutoff $\Delta_{\rm max}$. In both the Chern-Simons theory, and in the $O(N)$ model at infinite $N$, we compute the current spectral functions analytically as a function of $\Delta_{\rm max}$ and reproduce previous results in the limit that the truncation $\Delta_{\rm max}$ is taken to $\infty$. Along the way, we determine how to preserve gauge invariance and how to choose an optimal discrete basis for the momenta of states in the truncation space.Comment: 32+25 pages, 8 figures. v2: updated ref

Duo: a general program for calculating spectra of diatomic molecules

Duo is a general, user-friendly program for computing rotational, rovibrational and rovibronic spectra of diatomic molecules. Duo solves the Schr\"{o}dinger equation for the motion of the nuclei not only for the simple case of uncoupled, isolated electronic states (typical for the ground state of closed-shell diatomics) but also for the general case of an arbitrary number and type of couplings between electronic states (typical for open-shell diatomics and excited states). Possible couplings include spin-orbit, angular momenta, spin-rotational and spin-spin. Corrections due to non-adiabatic effects can be accounted for by introducing the relevant couplings using so-called Born-Oppenheimer breakdown curves. Duo requires user-specified potential energy curves and, if relevant, dipole moment, coupling and correction curves. From these it computes energy levels, line positions and line intensities. Several analytic forms plus interpolation and extrapolation options are available for representation of the curves. Duo can refine potential energy and coupling curves to best reproduce reference data such as experimental energy levels or line positions. Duo is provided as a Fortran 2003 program and has been tested under a variety of operating systems

Pension schemes versus real estate

The demographic, economic and social changes that have characterized the last decades, and the dramatic financial crisis that has taken place since 2008, have led to a demand for structural changes in the pension sector and a growing interest in individual pension products. Hence the need, for most elderly people, to liquidate their fixed assets, which are usually the homes in which they live. This highlights products such as reverse mortgages and domestic reversibility plans. Within this context, we propose a contractual scheme where an immediate life annuity is obtained by paying a single-premium in the form of real estate rights (RERs), for example by transferring to an insurer the property title of a house or a similar realty, while keeping its usufruct or a restricted bundle of rights. The level of the installments depends on the fair value of the transferred RER at the contract’s issue, the life expectancy of the insured and the expected growth rate of the real estate market value. The contract design is developed by considering the control of the financial risk inherent in the contract itself, because of the prospective changes in the value of the RERs, and the level of the insurer’s leverage. Finally, we provide some numerical evidence of the proposed contractual structure, in order to compare the level of the installments according to the house return forecasts in different European countries

Relaxation time spectrum of low-energy excitations in one- and two-dimensional materials with charge or spin density waves

The long-time thermal relaxation of (TMTTF)$_2$Br, Sr$_{14}$Cu$_{24}$O$_{41}$ and Sr$_2$Ca$_{12}$Cu$_{24}$O$_{41}$ single crystals at temperatures below 1 K and magnetic field up to 10 T is investigated. The data allow us to determine the relaxation time spectrum of the low energy excitations caused by the charge-density wave (CDW) or spin-density wave (SDW). The relaxation time is mainly determined by a thermal activated process for all investigated materials. The maximum relaxation time increases with increasing magnetic field. The distribution of barrier heights corresponds to one or two Gaussian functions. The doping of Sr$_{14-x}$Ca$_{x}$Cu$_{24}$O$_{41}$ with Ca leads to a drastic shift of the relaxation time spectrum to longer time. The maximum relaxation time changes from 50 s (x = 0) to 3000 s (x = 12) at 0.1 K and 10 T. The observed thermal relaxation at x=12 clearly indicates the formation of the SDW ground state at low temperatures