Related papers: Generating functions and sum rules for quantum osc…
The generating function of a Hamiltonian $H$ is defined as $F(t)=\langle e^{-itH}\rangle$, where $t$ is the time and where the expectation value is taken on a given initial quantum state. This function gives access to the different moments…
We formulate exact generalized nonequilibrium fluctuation relations for the quantum mechanical harmonic oscillator coupled to multiple harmonic baths. Each of the different baths is prepared in its own individual (in general nonthermal)…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
The familiar generating functionals in quantum field theory fail to be true measures and, so they make the sense only in the framework of the perturbation theory. In our approach, generating functionals are defined strictly as the Fourier…
Various aspects of the statistics of work performed by an external classical force on a quantum mechanical system are elucidated for a driven harmonic oscillator. In this special case two parameters are introduced that are sufficient to…
Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The…
Sum rules -- relating the static quark potential V(R) to the spatial distribution of the action and energy in the colour fields of flux-tubes -- are applied in three ways: 1) To extract generalised beta-functions: 2) As a consistency check…
In the isovector reaction, the sum rule for the spin dependent function $g_1$ which is related to the cross section of the photoproduction is derived. In the small $Q^2$ region, the sum rule is dominated by the low energy contribution and…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…
We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A…
Given are a first principles derivation and formulation of the probabilistic concepts that underly equilibrium quantum statistical mechanics. The transition to non-equilibrium probability is traversed briefly.
We develop a new formalism for constructing probabilities associated to the causal ordering of events in quantum theory, where by an event we mean the emergence of a measurement record on a detector. We start with constructing probabilities…
We demonstrate a quantum regime of dissipative nonlinear oscillator where creation of Fock states as well as superpositions of Fock states are realized for time-intervals exceeding the characteristic decoherence time. Preparation of quantum…
It is shown that it is possible to establish sum rules that must be satisfied at the nodes and extrema of the eigenstates of confining potentials which are functions of a single variable. At any boundstate energy the Schroedinger equation…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
The gap probability generating function has as its coefficients the probability of an interval containing exactly $k$ eigenvalues. For scaled random matrices with orthogonal symmetry, and the interval at the hard or soft spectrum edge, the…
Quantum simulation of complex quantum systems and their properties often requires the ability to prepare initial states in an eigenstate of the Hamiltonian to be simulated. In addition, to compute the eigenvalues of a Hamiltonian is in…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…