Related papers: Completely Positive Markovian Quantum Dynamics in …
We present updated constraints on an interacting dark energy - dark matter model with pure momentum transfer, where dark energy is in the form of a quintessence scalar field with an exponential potential. We run a suite of MCMC analyses…
In this paper, we study the controllability and stabilizability properties of the Kolmogorov forward equation of a continuous time Markov chain (CTMC) evolving on a finite state space, using the transition rates as the control parameters.…
It is known that the longitudinal and transverse excitation modes can exist in the vicinity of a quantum critical point in the ordered phase of quantum magnetic systems. The total moment sum rule for such systems is derived on the basis of…
We define a perturbative approximation for the solution of Lindblad master equations with time-dependent generators that satisfies the fundamental property of complete positivity, as essential for quantum simulations and optimal control.…
Manipulation of a quantum system requires the knowledge of how it evolves. To impose that the dynamics of a system becomes a particular target operation (for any preparation of the system), it may be more useful to have an equation of…
Many problems in quantum dynamics can be cast as the decay of a single quantum state into a continuum. The time-dependent overlap with the initial state, called the fidelity, characterizes this decay. We derive an analytic expression for…
An important class of resonance problems involves the study of perturbations of systems having embedded eigenvalues in their continuous spectrum. Problems with this mathematical structure arise in the study of many physical systems, e.g.…
We propose a novel non-compact, positivity-preserving scheme for linear non-divergence form parabolic equations. Based on the Feynman-Kac formula, the solution is expressed as a conditional expectation of an associated diffusion process.…
We consider several observers who monitor different parts of the environment of a single quantum system and use their data to deduce its state. We derive a set of conditional stochastic master equations that describe the evolution of the…
A finite quantum system S is coupled to a thermal, bosonic reservoir R. Initial SR states are possibly correlated, obtained by applying a quantum operation taken from a large class, to the uncoupled equilibrium state. We show that the full…
The weak-strong uniqueness of solutions to a broad class of cross-diffusion systems with volume filling is established. In general, the diffusion matrices are neither symmetric nor positive definite. This issue is overcome by supposing that…
We consider quantum systems with energy constraints relative to a reference Hamiltonian. In general, quantum channels and continuous-time dynamics need not satisfy energy conservation. Physically meaningful channels, however, only introduce…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
Many-body states described by a Schr\"{o}dinger equation include states of overlapping waves of non-vanishing interaction energies. These peculiar states formed in many-body transitions remain in asymptotic regions, and lead a new component…
Weak KAM theory for discount Hamilton-Jacobi equations and corresponding discount Lagrangian/Hamiltonian dynamics is developed. Then it is applied to error estimates for viscosity solutions in the vanishing discount process. The main…
The conditions under which quantum-classical Liouville dynamics may be reduced to a master equation are investigated. Systems that can be partitioned into a quantum-classical subsystem interacting with a classical bath are considered.…
We give an extended review of recent work on the extended weak coupling limit. Background material on completely positive semigroups and their unitary dilations is given, as well as a particularly easy construction of `quadratic noises'.
Decoherence is often modeled using Markovian master equations that predict exponential suppression of coherence and are frequently used as effective bounds on quantum behavior in complex environments. Such descriptions, however, correspond…
Let $\{Y_i,-\infty<i<\infty\}$ be a doubly infinite sequence of identically distributed, negatively dependent random variables under sub-linear expectations, $\{a_i,-\infty<i<\infty\}$ be an absolutely summable sequence of real numbers. In…
Recent results obtained from B decays on the phases of weak couplings described by the Cabibbo-Kobayashi-Maskawa (CKM) matrix are discussed, with particular emphasis on $\alpha$ and $\gamma = \pi - \beta - \alpha$.