Related papers: Meixner random variables and their quantum operato…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
In quantum mechanics, the operator representing the displacement of a system in position or momentum is always accompanied by a path-dependent phase factor. In particular, two non-parallel displacements in phase space do not compose…
A definition of $d$--dimensional $n$--Meixner random vectors is given first. This definition involves the commutators of their semi--quantum operators. After that we will focus on the $1$-Meixner random vectors, and derive a system of $d$…
We study the probability assignment for the outcomes of time-extended measurements. We construct the class-operator that incorporates the information about a generic time-smeared quantity. These class-operators are employed for the…
I consider random Schr\"odinger operators with exponentially decaying single site potential, which is allowed to change sign. For this model, I prove Anderson localization both in the sense of exponentially decaying eigenfunctions and…
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in…
Based on a quantum mechanical approach, we investigate moment- (or M-) indeterminate probability densities by way of the characteristic function and self-adjoint operators. The approach leads to new methods to construct classes of…
Partial symplectic conditional and joint probability representations of quantum mechanics are considered. The correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators are…
Exponential operator decompositions are an important tool in many fields of physics, for example, in quantum control, quantum computation, or condensed matter physics. In this work, we present a method for obtaining such decompositions,…
We put forward an interpretation of scalar quantum field theory as relativistic quantum mechanics by curing well known problems related to locality. A probabilistic interpretation of quantum field theory similar to quantum mechanics is…
Quantum harmonic analysis on phase space is shown to be linked with localization operators. The convolution between operators and the convolution between a function and an operator provide a conceptual framework for the theory of…
We consider the time-independent Wigner functions of phase-space quantum mechanics (a.k.a. deformation quantization) for a Morse potential. First, we find them by solving the $\ast$-eigenvalue equations, using a method that can be applied…
Using a position operator obtained for spin 1 particles by the present author and Wigner, we obtain a quantum relativistic result for the hidden momentum force experienced by particles with structure. In particular, our result applies to…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
We study the phenomenon of composite operator renormalization and mixing in systems where time-translational invariance is broken and the evolution is out-of-equilibrium. We show that composite operators mix also through non-local memory…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the…
Partial transpose is an important operation for quantifying the entanglement, here we study the (partial) transpose of any single (two-mode) operators. Using the Fock-basis expansion, it is found that the transposed operator of an arbitrary…
We present a method for calculating expectation values of operators in terms of a corresponding c-function formalism which is not the Wigner--Weyl position-momentum phase-space, but another space. Here, the quantity representing the quantum…