Exact energy spectrum of a two-temperature kinetic Ising model

The exact energy spectrum is developed for a two temperature kinetic Ising spin chain, and its dual reaction diffusion system with spatially alternating pair annihilation and creation rates. Symmetries of the system pseudo-Hamiltonian that enable calculation of the spectrum are also used to derive explicit state vectors for small system sizes, and to make observations regarding state vectors in the general case. Physical consequences of the surprisingly simple form for the eigenvalues are also discussed

Stochastic epidemic-type model with enhanced connectivity: exact solution

We present an exact analytical solution to a one-dimensional model of the Susceptible-Infected-Recovered (SIR) epidemic type, with infection rates dependent on nearest-neighbor occupations. We use a quantum mechanical approach, transforming the master equation via a quantum spin operator formulation. We calculate exactly the time-dependent density of infected, recovered and susceptible populations for random initial conditions, and compare our results with a low connectivity SIR model reported by Schuetz et al.. Our results compare well to those of previous work, validating the model as a useful tool for additional and extended studies in this important area. Our model also provides exact solutions for the n-point correlation functions, and can be extended to more complex epidemic type models

Cooperative sequential adsorption models on a Cayley tree: analytical results and applications

We present a class of cooperative sequential adsorption models on a Cayley tree with constant and variable attachment rates and their possible applications for ionic self-assembly of thin films and drug encapsulation of nanoparticles. Using the empty interval method, and generalizing results known from reaction-diffusion processes on Cayley trees, we calculate a variety of quantities such as time-dependent surface coverage and time-dependent probabilities of certain particle configurations

Non-equilibrium statistical mechanics: a solvable model

A two-temperature linear spin model is presented that allows an easily understandable introduction to non-equilibrium statistical physics. The model is one that includes the concepts that are typical of more realistic non-equilibrium models but that allows straightforward steady state solutions and, for small systems, development of the full time dependence for configuration probabilities. The model is easily accessible to upper-level undergraduate students, and also provides a good check for computer models of larger systems

Modal beam splitter:Determination of the transversal components of an electromagnetic light field

The transversal profile of beams can always be defined as a superposition of orthogonal fields, such as optical eigenmodes. Here, we describe a generic method to separate the individual components in a laser beam and map each mode onto its designated detector with low crosstalk. We demonstrate this with the decomposition into Laguerre-Gaussian beams and introduce a distribution over the integer numbers corresponding to the discrete orbital and radial momentum components of the light field. The method is based on determining an eigenmask filter transforming the incident optical eigenmodes to position eigenmodes enabling the detection of the state of the light field using single detectors while minimizing cross talk with respect to the set of filter masks considered.UK Engineering and Physical Sciences Research Council [EP/J01771X/1]This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Making the most of interference : speckle metrology and its application to cold atoms

Speckle patterns result from the interference of multiple reflections in disordered media. This is regarded as a randomization process which destroys information contained within the initial light beam and is deleterious to many optical systems. Indeed, many engineers study speckle to remove its effect. Intriguingly however, the processes that produce the speckle are entirely linear, and there is growing recognition that this complex pattern is rich in useful information on both the incident laser source and the environment, with startling potential uses. We will demonstrate our recent results [1], which show that the speckle pattern produced by light propagation in an integrating sphere can be used as a sensitive wavemeter, with a resolution below 1fm. Moreover, this can be used to stabilize the wavelength of a laser on a timescale and to a stability applicable for laser cooling of cold atoms. Reference: [1] N. K. Metzger, et al., “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization”, Nature Communications 8, 15610 (2017)PostprintNon peer reviewe

Non-equilibrium stationary state of a two-temperature spin chain

A kinetic one-dimensional Ising model is coupled to two heat baths, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($$). Spin flips occur with Glauber-type rates generalised to the case of two temperatures. Driven by the temperature differential, the spin chain settles into a non-equilibrium steady state which corresponds to the stationary solution of a master equation. We construct a perturbation expansion of this master equation in terms of the temperature difference and compute explicitly the first two corrections to the equilibrium Boltzmann distribution. The key result is the emergence of additional spin operators in the steady state, increasing in spatial range and order of spin products. We comment on the violation of detailed balance and entropy production in the steady state.Comment: 11 pages, 1 figure, Revte

Suppression of matching field effects by splay and pinning energy dispersion in YBa_2Cu_3O_7 with columnar defects

We report measurements of the irreversible magnetization M_i of a large number of YBa_2Cu_3O_7 single crystals with columnar defects (CD). Some of them exhibit a maximum in M_i when the density of vortices equals the density of tracks, at temperatures above 40K. We show that the observation of these matching field effects is constrained to those crystals where the orientational and pinning energy dispersion of the CD system lies below a certain threshold. The amount of such dispersion is determined by the mass and energy of the irradiation ions, and by the crystal thickness. Time relaxation measurements show that the matching effects are associated with a reduction of the creep rate, and occur deep into the collective pinning regime.Comment: 7 pages, 5 figures, submitted to Phys. Rev.