Equilibrium Stochastic Delay Processes

Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is available for linear models only. We introduce a class of stochastic delay processes with nonlinear time-local forces and linear time-delayed forces that obey fluctuation theorems and converge to a Boltzmann equilibrium at long times. From the point of view of control theory, such ``equilibrium stochastic delay processes'' are stable and energetically passive, by construction. Computationally, they provide diverse exact constraints on general nonlinear stochastic delay problems and can, in various situations, serve as a starting point for their perturbative analysis. Physically, they admit an interpretation in terms of an underdamped Brownian particle that is either subjected to a time-local force in a non-Markovian thermal bath or to a delayed feedback force in a Markovian thermal bath. We illustrate these properties numerically for a setup familiar from feedback cooling and point out experimental implications.

Non-adiabatic modulation of premixed-flame thermoacoustic frequencies in slender tubes

This paper presents an experimental study of the influence of heat losses on the onset of thermoacoustic instabilities in methane–air premixed flames propagating in a horizontal tube of diameter, $D = 10$ mm. Flames are ignited at the open end of the tube and propagate towards the closed end undergoing strong oscillations of different features owing to the interaction with acoustic waves. The frequency of oscillation and its axial location are controlled through the tube length $L$ and the intensity of heat losses. These parameters are respectively modified in the experiments by a moveable piston and a circulating thermal bath of water prescribing temperature conditions. Main experimental observations show that classical one-dimensional predictions of the oscillation frequency do not accurately describe the phenomena under non-adiabatic real scenarios. In addition to the experimental measurements, a quasi-one-dimensional analysis of the burnt gases is provided, which introduces the effect of heat losses at the wall of the tube on the interplay between the acoustic field and the reaction sheet. As a result, this analysis provides an improved description of the interaction and accurately predicts the excited flame-oscillation harmonics through the eigenvalues of the non-adiabatic acoustics model. Unlike the original one-dimensional analysis, the comparison between the flame oscillation frequency provided by the non-adiabatic extended theory and the frequencies measured in our experiments is in excellent agreement in the whole range of temperatures considered. This confirms the importance of heat losses in the modulation of the instabilities and the transition between different flame oscillation regimes.

Dynamics of Open Quantum Systems I, Oscillation and Decay

We develop a framework to analyze the dynamics of a finite-dimensional quantum system S in contact with a reservoir R. The full, interacting SR dynamics is unitary. The reservoir has a stationary state but otherwise dissipative dynamics. We identify a main part of the full dynamics, which approximates it for small values of the SR coupling constant, uniformly for all times t≥0. The main part consists of explicit oscillating and decaying parts. We show that the reduced system evolution is Markovian for all times. The technical novelty is a detailed analysis of the link between the dynamics and the spectral properties of the generator of the SR dynamics, based on Mourre theory. We allow for SR interactions with little regularity, meaning that the decay of the reservoir correlation function only needs to be polynomial in time, improving on the previously required exponential decay.In this work we distill the structural and technical ingredients causing the characteristic features of oscillation and decay of the SR dynamics. In the companion paper [27] we apply the formalism to the concrete case of an N-level system linearly coupled to a spatially infinitely extended thermal bath of non-interacting Bosons.

Cannibalism's lingering imprint on the matter power spectrum

The early universe may have contained internally thermalized dark sectors that were decoupled from the Standard Model. In such scenarios, the relic dark thermal bath, composed of the lightest particle in the dark sector, can give rise to an epoch of early matter domination prior to Big Bang Nucleosynthesis, which has a potentially observable impact on the smallest dark matter structures. This lightest dark particle can easily and generically have number-changing self-interactions that give rise to “cannibal” behavior. We consider cosmologies where an initially sub-dominant cannibal species comes to temporarily drive the expansion of the universe, and we provide a simple map between the particle properties of the cannibal species and the key features of the enhanced dark matter perturbation growth in such cosmologies. We further demonstrate that cannibal self-interactions can determine the small-scale cutoff in the matter power spectrum even when the cannibal self-interactions freeze out prior to cannibal domination.

Hard gluon evolution in warming medium

We describe the energy distribution of hard gluons travelling through a dense quark–gluon plasma whose temperature increases linearly with time, within a probabilistic perturbative approach. The results were applied to the thermalization problem in heavy ion collisions. In the weak coupling picture this thermalization occurs from “the bottom up”: high energy partons, formed early in the collision, radiate low energy gluons which then proceed to equilibrate among themselves, forming a thermal bath that brings the high energy sector to equilibrium. We see that, in this scenario, the dynamic we describe must set in around $$t \sim 0.5$$ t ∼ 0.5 fm/c after the collision in order to reach a fully thermalized state at $$t \sim 1$$ t ∼ 1 fm/c. We then look at the entropy density and average temperature of the soft thermal bath, as the system approaches (local) thermal equilibrium.

Landauer’s Principle of Minimum Energy Might Place Limits on the Detectability of Gravitons of Certain Mass

According to Landauer’s principle, the energy of a particle may be used to record or erase N number of information bits within the thermal bath. The maximum number of information N recorded by the particle in the heat bath is found to be inversely proportional to its temperature T. If at least one bit of information is transferred from the particle to the medium, then the particle might exchange information with the medium. Therefore for at least one bit of information, the limiting mass that can carry or transform information assuming a temperature T= 2.73 K is equal to m = 4.718´10-40 kg which is many orders of magnitude smaller that the masse of most of today’s elementary particles. Next, using the corresponding temperature of a graviton relic and assuming at least one bit of information the corresponding graviton mass is calculated and from that, a relation for the number of information N carried by a graviton as a function of the graviton mass mgr is derived. Furthermore, the range of information number contained in a graviton is also calculated for the given range of graviton mass as given by Nieto and Goldhaber, from which we find that the range of the graviton is inversely proportional to the information number N. Finally, treating the gravitons as harmonic oscillators in an enclosure of size R we derive the range of a graviton as a function of the cosmological parameters in the present era.

Hard gluon evolution in the last stage of the bottom-up thermalization

The study of how fast thermalization in heavy ion collisions occurs has been one of the central topics in the heavy ion community. In the weak coupling picture this thermalization occurs from “the bottom up”: high energy partons, formed early in the collision, radiate low energy gluons which then proceed to equilibrate among themselves, forming a thermal bath that brings the high energy sector to equilibrium. In this scheme we apply a model on parton energy loss to discuss the effects of medium expansion on the thermalization problem and estimate the average transverse momentum diffusivity for thermalization in a Bjorken expanding medium.

Ergotropy from quantum and classical correlations

It is an established fact that quantum coherences have thermodynamic value. The natural question arises, whether other genuine quantum properties such as entanglement can also be exploited to extract thermodynamic work. In the present analysis, we show that the ergotropy can be expressed as a function of the quantum mutual information, which demonstrates the contributions to the extractable work from classical and quantum correlations. More specifically, we analyze bipartite quantum systems with locally thermal states, such that the only contribution to the ergotropy originates in the correlations. Our findings are illustrated for a two-qubit system collectively coupled to a thermal bath.

Lindblad Dynamics and Disentanglement in Multi-Mode Bosonic Systems

In this paper, we consider the thermal bath Lindblad master equation to describe the quantum nonunitary dynamics of quantum states in a multi-mode bosonic system. For the two-mode bosonic system interacting with an environment, we analyse how both the coupling between the modes and the coupling with the environment characterised by the frequency and the relaxation rate vectors affect dynamics of the entanglement. We discuss how the revivals of entanglement can be induced by the dynamic coupling between the different modes. For the system, initially prepared in a two-mode squeezed state, we find the logarithmic negativity as defined by the magnitude and orientation of the frequency and the relaxation rate vectors. We show that, in the regime of finite-time disentanglement, reorientation of the relaxation rate vector may significantly increase the time of disentanglement.