Related papers: Time inhomogeneous quantum dynamical maps
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
Time-reversal symmetry is of fundamental importance to physics. In the classical theory of time-reversal symmetry, the time-reversal symmetry of a quantum system is described by an anti-unitary operator, which is known as the time-reversal…
We study families of dynamical maps generated from interactions with varying degrees of symmetry. For a family of time-independent Hamiltonians, we demonstrate the relationship between symmetry, strong-coupling, perfect entanglers,…
We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of 'indivisible'…
We consider deterministic homogenization (convergence to a stochastic differential equation) for multiscale systems of the form \[ x_{k+1} = x_k + n^{-1} a_n(x_k,y_k) + n^{-1/2} b_n(x_k,y_k), \quad y_{k+1} = T_n y_k, \] where the fast…
In the strong noise regime, we study the homogeneization of quantum trajectories i.e. stochastic processes appearing in the context of quantum measurement. When the generator of the average semi-group can be separated into three distinct…
The description of the dynamics of an open quantum system in the presence of initial correlations with the environment needs different mathematical tools than the standard approach to reduced dynamics, which is based on the use of a…
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable…
We investigate the interplay between nonlinearity and inhomogeneities in discrete-time quantum walks on one-dimensional lattices. Nonlinear effects are introduced through a Kerr-like, intensity-dependent local phase, while spatial and…
The time reversal of a completely-positive, nonequilibrium discrete-time quantum Markov evolution is derived via a suitable adjointness relation. Space-time harmonic processes are introduced for the forward and reverse-time transition…
Inhomogeneous space-times in loop quantum cosmology have come under better control with recent advances in effective methods. Even highly inhomogeneous situations, for which multiverse scenarios provide extreme examples, can now be…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
Quantum speed limit time defines the limit on the minimum time required for a quantum system to evolve between two states. Investigation of bounds on speed limit time of quantum system under non-unitary evolution is of fundamental interest,…
We survey the equations of continuous-time quantum walks on simple one-dimensional lattices, which include the finite and infinite lines and the finite cycle, and compare them with the classical continuous-time Markov chains. The focus of…
In the covariant canonical approach to classical physics, each point in phase space represents an entire classical trajectory. Initial data at a fixed time serve as coordinates for this ``timeless'' phase space, and time evolution can be…
We study the dynamics of quantum systems interacting with a stream of entangled qubits. Under fairly general conditions, we present a detailed framework describing the conditional dynamical maps for the system, called quantum trajectories,…
To our knowledge, the populations are generally assumed to be homogeneous in the traditional approach to evolutionary game dynamics. Here, we focus on the inhomogeneous populations. A simple model which can describe the inhomogeneity of the…
Quantum stochastic master equations of jump type are formulated in a general way and connections with quantum/classical hybrid systems and quantum filtering theory are discussed. By introducing the notion of ``typical trajectory", we show…