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We construct the higher genus Open-Closed Gromov-Witten potential as a solution of the quantum master equation defined up to quantum master isotopy.
Master equations are commonly used to describe time evolution of open systems. We introduce a general method for calculating a Markovian solution of the Nakajima-Zwanzig generalized master equation. We do so for a time dependent transport…
We provide a formula for computing the overlap between two Generalized Coherent States of any rank one simple Lie algebra. Then, we apply our formula to spin coherent states (i.e. $\mathfrak{su}(2)$ algebra), pseudo-spin coherent states…
This paper is dedicated to a detailed analysis and computation of quantum states of causal fermion systems. The mathematical core is to compute integrals over the unitary group asymptotically for a large dimension of the group, for various…
A set of operators, the so-called k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of an algebra arising from two non-commuting quon algebras. The deformation parameters q…
We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general…
This paper addresses new results on the factorization of the general Heun's operator, extending the investigations performed in previous works [{\it Applied Mathematics and Computation} {\bf 141} (2003), 177 - 184 and {\bf 189} (2007), 816…
A generalization of the quantum van der Waals equation of state for a multi-component system in the grand canonical ensemble is proposed. The model includes quantum statistical effects and allows to specify the parameters characterizing…
This paper is devoted to path-dependent kinetics equations arising, in particular, from the analysis of the coupled backward - forward systems of equations of mean field games. We present local well-posedness, global existence and some…
A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular…
We extend the Van der Waals equation of state to a universal form and find that the van der Waals equation of state is a special condition of this form. Then a good form of the equation of state for a balanced liquid-gas coexistence…
Ultrastrong light-matter interaction in an optomechanical system can result in nonlinear optical effects such as photon blockade. The system-bath couplings in such systems play an essential role in observing these effects. Here we study the…
A description of generalized coherent states and geometric phases in the light of the general theory of smooth loops is given.
A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…
We present comparison principles, Lipschitz estimates and study state constraints problems for degenerate, second-order Hamilton-Jacobi equations.
Superpartner correspondence of states of colored particle in external chromomagnetic field given by non-commuting constant vector potentials is determined. Squared Dirac equation for this particle is solved exactly and explicit expressions…
On a finite regular graph, (co)resonant states are eigendistributions of the transfer operator associated to the shift on one-sided infinite non-backtracking paths. We introduce two pairings of resonant and coresonant states, the vertex…
A master equation approach to molecular motors allows to describe a mechano-chemical cyclic system where chemical and translational degrees of freedom are treated on an equal footing. A generalized detailed balance condition in the out of…
We consider a number of generalizations of the $\beta$-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations or derangements…
We propose an explicit formula for an entanglement measure of pure multipartite quantum states, then study a general pure tripartite state in detail, and at end we give some simple but illustrative examples on four-qubits and m-qubits…