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A pedagogical derivation of statistical mechanics from quantum mechanics is provided, by means of open quantum systems. Besides, a new definition of Boltzmann entropy for a quantum closed system is also given to count microstates in a way…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
In this paper we develop numerical pricing methodologies for European style Exchange Options written on a pair of correlated assets, in a market with finite liquidity. In contrast to the standard multi-asset Black-Scholes framework, trading…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers.…
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…
We propose a tomographic approach to study quantum nonlocality in continuous variable quantum systems. On one hand we derive a Bell-like inequality for measured tomograms. On the other hand, we introduce pseudospin operators whose…
This paper deals with an extension of the so-called Black-Scholes model in which the volatility is modeled by a linear combination of the components of the solution of a differential equation driven by a fractional Brownian motion of Hurst…
The calculation of physical quantities by lattice QCD simulations requires in some important cases the determination of the inverse of a very large matrix. In this article we describe how stochastic estimator methods can be applied to this…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…
Interpretation of the nonclassical total probability formula arising in some quantum experiments is provided based on stochastic models described by means of a sequence of random vectors changing in the measurement procedures.
A dynamical quantum model assigns an eigenstate to a specified observable even when no measurement is made, and gives a stochastic evolution rule for that eigenstate. Such a model yields a distribution over classical histories of a quantum…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…
A new idea for the quantization of dynamic systems, as well as space time itself, using a stochastic metric is proposed. The quantum mechanics of a mass point is constructed on a space time manifold using a stochastic metric. A stochastic…
We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
Quantum dynamics simulations can be improved using novel quasiprobability distributions based on non-orthogonal hermitian kernel operators. This introduces arbitrary functions (gauges) into the stochastic equations, which can be used to…