Equilibrium fluctuations in maximally noisy extended quantum systems

We introduce and study a class of models of free fermions hopping between neighbouring sites with random Brownian amplitudes. These simple models describe stochastic, diffusive, quantum, unitary dynamics. We focus on periodic boundary conditions and derive the complete stationary distribution of the system. It is proven that the generating function of the latter is provided by an integral with respect to the unitary Haar measure, known as the Harish-Chandra-Itzykson-Zuber integral in random matrix theory, which allows us to access all fluctuations of the system state. The steady state is characterized by non trivial correlations which have a topological nature. Diagrammatic tools appropriate for the study of these correlations are presented. In the thermodynamic large system size limit, the system approaches a non random, self averaging, equilibrium state plus occupancy and coherence fluctuations of magnitude scaling proportionally with the inverse of the square root of the volume. The large deviation function for those fluctuations is determined. Although decoherence is effective on the mean steady state, we observe that sub-leading fluctuating coherences are dynamically produced from the inhomogeneities of the initial occupancy profile.

Non-monotonicity of Fano factor in a stochastic model for protein expression with sequesterisation at decoy binding sites

We present a stochastic model motivated by gene expression which incorporates unspecific interactions between proteins and binding sites. We focus on characterizing the distribution of free (i.e. unbound) protein molecules in a cell. Although it cannot be expressed in a closed form, we present three different approaches to obtain it: stochastic simulation algorithms, system of ODEs and quasi-steadystate solution. Additionally we use a large-system-size scaling to derive statistical measures of approximate distribution of the amount of free protein, such as the Fano factor. Intriguingly, we report that while in theabsence of or in the excess of decoy binding sites the Fano factor is equal to one (suggestive of Poissonian fluctuations), in the intermediate regimes of moderatelevels of binding sites the Fano factor is greater than one (suggestive of super-Poissonian fluctuations). We support and illustrate all of our results with numerical simulations.

Classical molecular dynamics investigations of biphenyl-based carbon nanomembranes

Background: Free-standing carbon nanomembranes (CNM) with molecular thickness and macroscopic size are fascinating objects both for fundamental reasons and for applications in nanotechnology. Although being made from simple and identical precursors their internal structure is not fully known and hard to simulate due to the large system size that is necessary to draw definite conclusions. Results: We performed large-scale classical molecular dynamics investigations of biphenyl-based carbon nanomembranes. We show that one-dimensional graphene-like stripes constitute a highly symmetric quasi one-dimensional energetically favorable ground state. This state does not cross-link. Instead cross-linked structures are formed from highly excited precursors with a sufficient amount of broken phenyls. Conclusion: The internal structure of the CNM is very likely described by a disordered metastable state which is formed in the energetic initial process of electron irradiation and depends on the process of relaxation into the sheet phase.

γ probe of nuclear dissipation

The Langevin model is applied to investigate the roles of excitation energy and system size in the evolution of post-saddle giant dipole resonance (GDR) γ-ray multiplicity (Mγ) with post-saddle friction strength (β). It is demonstrated that Mγ is more sensitive to β at high energy. Furthermore, it is shown that the dependence of γ emission on friction is sensitive to the size of fissioning nuclei, and a large system size significantly increases the sensitivity. Our findings indicate that in experiments, to tightly constrain post-saddle dissipation through the γ probe, it is optimal to produce heavy fissioning systems with high energy.

HEAT CONDUCTION IN ONE-DIMENSIONAL LATTICE WITH DOUBLE-WELL INTERACTION

Heat conduction in one-dimensional lattice with double-well interaction potential is studied numerically in different temperature regions. In the low temperature case, different structures such as order, period-2, and disorder structure phases, lead to different anomalous heat conduction. In a shallow intermediate temperature region, the heat conductivity is finite in a large system size. When temperature increases high enough, the heat conduction is anomalous, as well as FPU-β model.

FLUCTUATIONS OF QUANTUM RANDOM WALKS ON CIRCLES

Temporal fluctuations in the Hadamard walk on circles are studied. A temporal standard deviation of probability that a quantum random walker is positive at a given site is introduced to manifest striking differences between quantum and classical random walks. An analytical expression of the temporal standard deviation on a circle with odd sites is shown and its asymptotic behavior is considered for large system size. In contrast with classical random walks, the temporal fluctuation of quantum random walks depends on the position and initial conditions, since temporal standard deviation of the classical case is zero for any site. It indicates that the temporal fluctuation of the Hadamard walk can be controlled.