Martin Tarlie - Academia.edu (original) (raw)

Papers by Martin Tarlie

Social Science Research Network, 2013

Basic volatility and predictability characteristics of the aggregate US stock market over the las... more Basic volatility and predictability characteristics of the aggregate US stock market over the last century can be understood in terms of the dynamic properties of mean reverting equity discount rates. Additionally, high prices in good times and low prices in bad times can be understood in terms of the dynamics of both equity discount rates and return on capital, and the negative correlation between them.

Physical review, Jul 23, 2001

The decay of unstable states when several metastable states are available for occupation is inves... more The decay of unstable states when several metastable states are available for occupation is investigated using path-integral techniques. Specifically, a method is described which allows the probabilities with which the metastable states are occupied to be calculated by finding optimal paths, and fluctuations about them, in the weak noise limit. The method is illustrated on a system described by two coupled Langevin equations, which are found in the study of instabilities in fluid dynamics and superconductivity. The problem involves a subtle interplay between non-linearities and noise, and a naive approximation scheme which does not take this into account is shown to be unsatisfactory. The use of optimal paths is briefly reviewed and then applied to finding the conditional probability of ending up in one of the metastable states, having begun in the unstable state. There are several aspects of the calculation which distinguish it from most others involving optimal paths: (i) the paths do not begin and end on an attractor, and moreover, the final point is to a large extent arbitrary, (ii) the interplay between the fluctuations and the leading order contribution are at the heart of the method, and (iii) the final result involves quantities which are not exponentially small in the noise strength. This final result, which gives the probability of a particular state being selected in terms of the parameters of the dynamics, is remarkably simple and agrees well with the results of numerical simulations. The method should be applicable to similar problems in a number of other areas such as state selection in lasers, activationless chemical reactions and population dynamics in fluctuating environments.

The problem of state selection when multiple metastable states compete for occupation is consider... more The problem of state selection when multiple metastable states compete for occupation is considered for systems that are accelerated far from equilibrium. The dynamics of the supercurrent in a narrow superconducting ring under the influence of an external electric field is used to illustrate the general phenomenology.

Proceedings of the National Academy of Sciences, 1998

We studied the dynamics of a Brownian particle moving in a spatially anisotropic potential acted ... more We studied the dynamics of a Brownian particle moving in a spatially anisotropic potential acted on by multiplicative temporal modulations so that V ( x , t ) = g ( t ) U ( x ). Using the concept of the “thermodynamic action,” we show that the class of modulation that maximizes the flow is a square-wave in time. We also show that adding a weak, homogenous force F in synergy with the square-wave modulation can cause particles of slightly different size to move in opposite directions. The synergetic change in velocity caused by F can be much greater than the drift velocity that would be caused by F alone.

Physical Review Letters, 1998

Physical Review Letters, 1996

Cryogenic scanning tunneling microscopy has been used as a local probe of the superconducting pro... more Cryogenic scanning tunneling microscopy has been used as a local probe of the superconducting proximity effect across a normal metal-superconductor interface of a short coherence length superconductor. Both the topography and the local electronic density of states were measured on a superconducting NbSe 2 crystal decorated with nanometer-size Au islands. The presence of a quasiparticle bound state could be inferred even when the probe was located directly on the bare NbSe 2 surface near an Au island, indicating a severe depression of the pair potential inside the superconductor due to the proximity effect. [S0031-9007(96)00754-5]

Physical Review E, 2005

A system consisting of two species in a fluctuating environment, when the interspecies competitio... more A system consisting of two species in a fluctuating environment, when the interspecies competition for resources is strong, will have a stochastic outcome: only one of the species will survive, but there is no a priori way of knowing which one this will be. It is natural in such a situation to ask what will be the probability of one or another of the species surviving. This probability is calculated as a function of the average growth rates and the strengths of the interaction between the species and of the randomness. This is an example of a class of stochastic problems in which multiple final states are available for occupation. We refer to the choice of final states as state selection, and the probabilities of final states being occupied as state-selection probabilities. The calculation of these probabilities is carried out in the context of a model of the system which consists of two coupled stochastic differential equations. By reformulating these equations in terms of path integrals, the powerful methods based on the use of optimal paths may be utilized to calculate the probability of one outcome or the other. The analytical results obtained by using this technique agree well with numerical simulations when both species have the same growth rate. Although the method adopted rests on the assumption that the strength of the fluctuations, D, is small, remarkably the analytic results are still found to be in good agreement with the numerical results when D is of order 1.

Physical Review E, 2004

The addition of noise to a dynamical system means that initial states near points of instability ... more The addition of noise to a dynamical system means that initial states near points of instability may no longer decay to a unique stable state. A common example of this behavior occurs in a dynamical system with two degrees of freedom and with two or more stable states. If the initial state of the system is near the separatrices bounding the basins of attraction of these stable states, then the addition of noise to the system means that there is a nonzero probability that the stable state selected is in a different basin of attraction to that of the initial state. We discuss a method of calculating these state-selection probabilities based on a path-integral representation of the stochastic dynamics. The relationship of this approach to a method based on the solution of the backward Fokker-Planck equation is particularly stressed, since this was used in previous studies of problems of this type. However, while the method based on the backward Fokker-Planck equation is a powerful one for systems with one degree of freedom, in systems with more degrees of freedom it is much less useful. Since the standard method of solution in this case involves a series of mappings onto a deterministic dynamics which is simply the classical dynamics associated with the path-integral formulation, we argue that for systems with more than one degree of freedom, the path-integral method is a very natural way of calculating state-selection probabilities. We illustrate this on a simple example taken from population biology, and find that the stateselection probabilities are in excellent agreement with Monte Carlo simulations.

The formalism which has been developed to give general expressions for the determinants of differ... more The formalism which has been developed to give general expressions for the determinants of differential operators is extended to the physically interesting situation where these operators have a zero mode which has been extracted. In the approach adopted here, this mode is removed by a novel regularisation procedure, which allows remarkably simple expressions for these determinants to be derived.

arXiv: Soft Condensed Matter, 1997