Related papers: Interaction representation method for Markov maste…
Quantum dynamics of driven open systems should be compatible with both quantum mechanic and thermodynamic principles. By formulating the thermodynamic principles in terms of a set of postulates we obtain a thermodynamically consistent…
Quantum timeless approaches solve the problem of time by recovering the usual unitary evolution of quantum theory relative to a clock in a stationary quantum Universe. For some Hamiltonians of the Universe, such as those including an…
Representation of classical dynamics by unitary transformations has been used to develop unified description of hybrid classical-quantum systems with particular type of interaction, and to formulate abstract systems interpolating between…
The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…
We consider Markovian open quantum dynamics with weak unitary symmetries. Starting from the quantum master equation for the system alone, it is known that the joint dynamics of the system and its environment can be obtained by dilation,…
We study a class of dynamical semigroups $(\mathbb{L}^n)_{n\in\mathbb{N}}$ that emerge, by a Feynman--Kac type formalism, from a random quantum dynamical system…
The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states…
In this paper, a simple geometric structure is shown, which underlies the interaction Hamiltonian of quantum electrodynamics. Specifically, eight parts of the interaction Hamiltonian, corresponding to eight basic Feynman diagrams, are found…
Starting from any proper action of any locally compact quantum group on any discrete quantum space, we show that its equivariant representation theory yields a concrete unitary 2-category of finite type Hilbert bimodules over the discrete…
The dynamics of finite dimension open quantum systems is studied with the help of the simplest possible form of projection operators, namely the ones which project only onto one dimensional subspaces. The simplicity of the action of the…
For any simple Lie algebra g and any complex number q which is not zero or a nontrivial root of unity, we construct a dynamical quantum group (Hopf algebroid), whose representation theory is essentially the same as the representation theory…
In this article, first we give two formulae for the delta invariant of a complex curve singularity that can be embedded as a ${\mathbb Q}$-Cartier divisor in a normal surface singularity with rational homology sphere link. Next, we consider…
We find that the quantum monodromy matrix associated with a derivative nonlinear Schrodinger (DNLS) model exhibits U(2) or U(1,1) symmetry depending on the sign of the related coupling constant. By using a variant of quantum inverse…
Among the discrete evolution equations describing a quantum system $\rH_S$ undergoing repeated quantum interactions with a chain of exterior systems, we study and characterize those which are directed by classical random variables in…
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
We introduce an alternative way to understand the decomposition of a quantum system into interacting parts and show that it is natural in several physical models. This enables us to define a reduced density operator for a working system…
We consider Markovian dynamics of a finitely dimensional open quantum system featuring a weak unitary symmetry, i.e., when the action of a unitary symmetry on the space of density matrices commutes with the master operator governing the…
We present an algebraic procedure for constructing Hamiltonians with several distinct partial dynamical symmetries (PDSs), of relevance to shape-coexistence phenomena. The procedure relies on a spectrum generating algebra encompassing…
Master equations describing open quantum dynamics are typically first order differential equations. When such dynamics brings the trajectories in state space of more than one initial state to the same point at finite instants in time, the…
The structure of uniformly continuous quantum Markov semigroups with atomic decoherence-free subalgebra is established providing a naturaldecomposition of a Markovian open quantum system into its noiseless (decoherence-free) and irreducible…