Related papers: Quantum L_p and Orlicz spaces
Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully…
This paper is a serious attempt at reconciling quantum and classical mechanics through the concept of dynamic space and the acceptance of non-zero Ricci tensor for vacuum. Starting with scalar particles, the paper shows that with those two…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
This paper establishes a categorical equivalence between the category $\mathbb{COL}$ of complete orthomodular lattices and the category $\mathscr{T}\mathbb{ODA}$ of $\mathscr{T}$-based orthomodular dynamic algebras. Complete orthomodular…
Presented is a quantum computing representation of Dirac particle dynamics. The approach employs an operator splitting method that is an analytically closed-form product decomposition of the unitary evolution operator. This allows the Dirac…
Open quantum systems are a rich area of research in the intersection of quantum mechanics and stochastic analysis. By considering a variety of master equations, we unify multiple views of autonomous and controlled open quantum systems and,…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
Applications to quantum gravity of some results in C*-algebras are developed. We open by describing why algebra may be an integral aspect of quantum gravity. By interpreting the inner automorphisms of a C*-algebra as families of parallel…
This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a…
We present a way of understanding the curvature of space-time, the basic philosophy being that the (linear) geometry of any space is determined by the (linear) functionals on the algebra(s) of any fields defined on the space. It is known…
Time-series analysis and network analysis are now used extensively in diverse areas of science. In this paper, we applythese techniques to quantum dynamics in an optomechanical system: specifically, the long-time dynamics of the mean photon…
General Theory of Relativity and Quantum theory gives two different description of the same mother nature in the big and small scale respectively. Mathematical languages of these two theories are entirely different, one is geometric while…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
By extending the method developed in our recent paper \cite{LM} we present the AQFT framework in terms of von Neumann algebras. In particular, this approach allows for a locally covariant categorical description of AQFT which moreover…
We study mirror symmetry (A-side vs B-side) in the framework of quantum differential systems. We focuse on the logarithmic and non-resonant case, which describes the geometric situation. We show that quantum differential systems provide a…
The quantum dynamics of a particle in the Modified P\"oschl-Teller potential is derived from the group $SL(2,R)$ by applying a Group Approach to Quantization (GAQ). The explicit form of the Hamiltonian as well as the ladder operators is…
This is an introduction to loop quantum cosmology (LQC) reviewing mini- and midisuperspace models as well as homogeneous and inhomogeneous effective dynamics.
Strong driving of quantum systems opens opportunities for both controlling and characterizing their states. For theoretical studying of these systems properties we use the rate-equation formalism. The advantage of such approach is its…
We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by…