Related papers: Elementary open quantum states
We first introduce and discuss density operator interpretations of quantum theory as a special case of a more general class of interpretations, giving special attention to a version that we call the `atomic version'. We then review some…
Master equations in the Lindblad form describe evolution of open quantum systems that is completely positive and simultaneously has a semigroup property. We analyze a possibility to derive this type of master equations from an intrinsically…
The dynamics of a quantum system coupled to a classical environment and subject to constraints that drive it out of equilibrium is described. The evolution of the system is governed by the quantum-classical Liouville equation. Rather than…
The three-particle operator in a second quantized form is studied. The operator is transformed into irreducible tensor form. Possible coupling schemes, distinguished by the classes of symmetric group \mathrm{S_{6}}, are presented.…
Crystal tensor operators, which tranform under U_q->0(sl(2)), in analogous way as the vectors of the crystal basis, are introduced. The Wigner-Eckart theorem for the crystal tensor is defined: the selection rules depend on the initial state…
We show that a noncommutative dynamical system of the type that occurs in quantum theory can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. The nature of these…
Many observers can simultaneously measure different parts of an environment of a quantum system in order to find out its state. To study this problem we generalize the formalism of conditional master equations to the multiple observer case.…
Evolution of coherent states is considered for a particle confined to a cylinder moving in a harmonic oscillator potential. Because of the discontinuous changes as time goes by of the phase representing the position of a particle on a…
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
We report a class of symmetry-intergable third-order evolution equations in 1+1 dimensions under the condition that the equations admit a second-order recursion operator that contains an adjoint symmetry (integrating factor) of order six.…
Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…
For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as…
Open quantum systems interact with their environment and their dynamical behaviour depends strongly both on the spectral properties of the environment and the structure of the interaction between the physical system and the environment. We…
This thesis presents studies performed on open quantum systems, that is, quantum systems interacting with their surrounding environment. Such systems are important not only in understanding the quantum-to-classical transition but also for…
We introduce families of one-dimensional Lindblad equations describing open many-particle quantum systems that are exactly solvable in the following sense: $(i)$ the space of operators splits into exponentially many (in system size)…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a…
Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic…
A (closed) dynamical system is a notion of how things can be, together with a notion of how they may change given how they are. The idea and mathematics of closed dynamical systems has proven incredibly useful in those sciences that can…
Dissipative quantum systems are sometimes phenomenologically described in terms of a non-hermitian hamiltonian $H$, with different left and right eigenvectors forming a bi-orthogonal basis. It is shown that the dynamics of waves in open…