Finite Non-zero Temperature Research Articles

Quantum field theory at finite temperature for 3D periodic backgrounds

The one-loop quantum corrections to the internal energy of some lattices due to the quantum fluctuations of the scalar field of phonons are studied. The band spectrum of the lattice is characterised in terms of the scattering data, allowing to compute the quantum vacuum interaction energy between nodes at zero temperature, as well as the total Helmholtz free energy, the entropy, and the Casimir pressure between nodes at finite non-zero temperature. Some examples of periodic potentials built from the repetition in one of the three spatial dimensions of the same punctual or compact supported potential are addressed: a stack of parallel plates constructed by positioning δδ′ -functions at the lattice nodes, and an ‘upside-down tiled roof’ of parallel two-dimensional Pöschl–Teller wells centred at the nodes. They will be called generalised Dirac comb and Pöschl–Teller comb, respectively. Positive one-loop quantum corrections to the entropy appear for both combs at non-zero temperatures. Moreover, the Casimir force between the lattice nodes is always repulsive for both chains when non-trivial temperatures are considered, implying that the primitive cell increases its size due to the quantum interaction of the phonon field.

Hartree–Fock analysis of the effects of long-range interactions on the Bose–Einstein condensation

We consider a Bose gas with two-body Kac-like scaled interactions where is a given repulsive and integrable potential, while is a positive parameter which controls the range of the interactions and their amplitude at a distance r. Using the Hartree–Fock (HF) approximation we find that, at finite non-zero temperatures, the Bose–Einstein (BE) condensation is destroyed by the repulsive interactions when they are sufficiently long-range. More precisely, we show that for sufficiently small but finite the off-diagonal part of the one-body density matrix always vanishes at large distances. Our analysis sheds light on the coupling between critical correlations and long-range interactions, which might lead to the breakdown of the off-diagonal long-range order even beyond the HF approximation. Furthermore, our HF analysis shows the existence of a threshold value above which the BE condensation is restored. Since is an unbounded increasing function of the temperature this implies for a fixed , namely for a fixed scaled potential, that a condensate cannot form above some critical temperature whatever the value of the density.

Quantum perspective on the localized strand separation and cyclization of DNA double helix

We apply Heisenberg model to study local strand separation and cyclization of double-stranded DNA molecule. By mapping the conformational properties of DNA onto the Heisenberg spin system, we show that denaturation can be viewed as a quench-induced quantum phase transition (QPT) at a finite non-zero temperature. These phase transitions lead to the formation of kinks in Heisenberg model that, in turn, correspond to sharp bends in helical axes of double-stranded DNA molecule. In this scenario we study the cyclization of DNA fragments of short length. Our results are in agreement with the reported observation that there is 1 open bp per circle of about 70 bp. Also we have computed the probability of the formation of kinks in circles of various sizes and have observed that beyond 100 bp it decreases sharply which is in agreement with experimental result.

Adiabatically deformed ensemble: Engineering nonthermal states of matter

We propose a route towards engineering non-thermal states of matter, which show largely unexplored physics. The main idea relies on the adiabatic passage of a thermal ensemble under slow variations of the system Hamiltonian. If the temperature of the initial thermal ensemble is either zero or infinite the ensemble after the passage is a simple thermal one with the same vanishing or infinite temperature. However, for any finite non-zero temperature intriguing non-thermal ensembles can be achieved. We exemplify this in: (a) a single oscillator (b) a dimerized interacting one dimensional chain of spinless fermions, (c) a BCS-type superconductor and (d) the topological Kitaev chain. We solve these models with a combination of methods; either exactly, numerically using the density matrix renormalization group (DMRG) or within an approximate functional renormalization group (FRG) scheme. The designed states show strongly non-thermal behavior in each of the considered models. For example, for the chain of spinless fermions we exemplify how long ranged non-thermal power-law correlations can be stabilized and for the Kitaev chain we elucidate how the non-thermal ensemble can largely alter the transition temperature separating topological and trivial phases.

Numerical simulation for finite deformation of single-walled carbon nanotubes at finite temperature using temperature-related higher order Cauchy-Born rule based quasi-continuum model

In the present study, a meshless computational framework for simulating the large deformation behaviors of single-walled carbon nanotubes (SWCNTs) at finite non-zero temperatures is established based on the so-called temperature-related higher order Cauchy-Born rule (THCB rule) where the second-order deformation gradient is involved in the kinematic description of the deformation of SWCNTs. The Helmholtz free energy is used as the thermodynamic potential and the local harmonic approximation (LHA) is adopted to construct the nanoscale quasi-continuum constitutive model. The proposed numerical approach is then applied to four numerical examples under different loading conditions. It is found that the results obtained by the proposed numerical framework agree well with those from molecular dynamics simulations.

Quantum-corrected black hole thermodynamics to all orders in the Planck length

We investigate the effects to all orders in the Planck length from a generalized uncertainty principle (GUP) on black holes thermodynamics. We calculate the corrected Hawking temperature, entropy, and examine in details the Hawking evaporation process. As a result, the evaporation process is accelerated and the evaporation end-point is a zero entropy, zero heat capacity and finite non-zero temperature black hole remnant (BHR). In particular we obtain a drastic reduction of the decay time, in comparison with the results obtained in the Hawking semi classical picture and with the GUP to leading order in the Planck length.

The U = ∞ Hubbard model with few holes: Monte Carlo studies near half-filling at non-zero temperatures

We present an efficient Monte Carlo method to study the properties of the infinitely repulsive Hubbard model with few holes at finite nonzero temperatures. Using this method, magnetic and specific heat results are presented for a 10 by 10 lattice with two holes. Our results show that the magnetization increases with decreasing temperature for such a finite system.

THE THERMODYNAMICS OF DYSLEXIC LEARNING

The dyslexic behaviour of a layered network is interpreted as arising from its incomplete training using a cost function that is sensitive to the grouping of Boolean functions into symmetry classes. The training is envisaged as a simulated annealing and a partial learning as the interruption of the cooling schedule at a finite nonzero temperature. We present the thermodynamics of the process. The onset of dyslexic and normal behaviours arise from phase transitions that take place during the annealing schedule. We exemplify the theory with the numerical analysis of a schematic model.