The dissipative harmonic oscillator has two representations. In the first representation the central oscillator couples with its position to an oscillator bath. In the second one it couples with its momentum to the bath. Both representations are related by a unitary transformation. If the...

The generalized Langevin equation (GLE) satisfied by harmonic oscillators coupled to a heat bath is transformed into an equality between the rate of energy dissipation and an extent of violation of the fluctuation-response relation. Its significance is discussed. When the system reaches a...

In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends portfolio analysis to the complex variable domain. This...

We test two methods to estimate a partition function of a system consisting of multi-atom molecules with intermolecular interaction. Our test case is a protein in water. The first method is based on rigid-body motions. The space in which the protein (bovine pancreatic trypsin inhibitor) would be...

A first-principles Monte Carlo code that exactly simulates quantum dynamics is presented which makes no use of amplitude calculations, only noise sources. The subtle question concerning how to map random choices in amplitude interferences is explained. In this formalism negative values of the...

The centred return on the London Stock Exchange's FTSE All Share Index is modelled as a simple harmonic oscillator with noise over the period from 1 January, 1994 until 30 June 2006. Our empirical results are compatible with the hypothesis that there is a period in the FTSE All Share Index of...

The first two moments of an underdamped harmonic oscillator were found for additive and multiplicative noises. A detailed analysis is performed of the case of a random damping which supplements the case of a random frequency which has received the most study. In both cases the second moments are...

We study statistical properties of the Hamiltonian (H=ωa†a+κa†N+1+κN+1a) generating phase state. Using the generalized Hellmann–Feynman theorem for ensemble average, we derive its mean energy and find the ratio of the mean energies contributed from the term a†a to that from...

Energy partition among many weakly coupled harmonic oscillators in equilibrium is found to be subject to 1/f fluctuations, and that the power spectral density (PSD) of fractional energy fluctuations of each oscillator is equal to 1/ω for frequency ω⪡γ, where γ is the simple relaxation...

This paper presents an empirical investigation of the intraday Brazilian stock market price fluctuations, considering q-Gaussian distributions that emerge from a non-extensive statistical mechanics. Our results show that, when price returns are measured over intervals less than one hour, the...