相关论文: Time Evolution of Typical Pure States from a Macro…

The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework.…

We derive a well-behaved nonlinear extension of the non-relativistic Liouville-von Neumann dynamics driven by maximal entropy production with conservation of energy and probability. The pure state limit reduces to the usual Schroedinger…

Hughston has recently proposed a stochastic extension of the Schr\"odinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a…

The phenomenological universalities (PU) are extended to include time-depended quantum oscillatory phenomena, coherence and supersymmetry. It will be proved that this approach generates minimum uncertainty coherent states of time-dependent…

Theories with ingredients like the Higgs mechanism, gravitons, and inflaton fields rejuvenate the idea that relativistic kinematics is dynamically emergent. Eternal inflation treats the Hubble constant H as depending on location.…

The dynamics in the onset of a Hagen-Poiseuille flow of an incompressible liquid in a channel of circular cross section is well-studied theoretically. We use an eigenfunction expansion in a Hilbert space formalism to generalize the results…

The simple harmonic oscillator has a well-known normalizable, positive energy, bound state spectrum. We show that degenerate with each such positive energy eigenvalue there is a non-normalizable positive energy eigenstate whose…

We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum-eigenstates of the system are |n(x)>.…

The circuit complexity of time-evolved pure quantum states grows linearly in time for an exponentially long time. This behavior has been proven in certain models, is conjectured to hold for generic quantum many-body systems, and is believed…

Time-asymmetric behavior as embodied in the second law of thermodynamics is observed in {\it individual macroscopic} systems. It can be understood as arising naturally from time-symmetric microscopic laws when account is taken of a) the…

The Master equation describes the time evolution of the probabilities of a system with a discrete state space. This time evolution approaches for long times a stationary state that will in general depend on the initial probability…

Classically, one could imagine a completely static space, thus without time. As is known, this picture is unconceivable in quantum physics due to vacuum fluctuations. The fundamental difference between the two frameworks is that classical…

The transition probability for time-dependent unitary evolution is invariant under the reversal of protocols just as in the classical Liouvillian dynamics. In this article, we generalize the expression of microscopic reversibility to…

We construct a complete set of Wannier functions which are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability…

Originating from the Hamiltonian of a single qubit system, the phenomenon of the avoided level crossing is ubiquitous in multiple branches of physics, including the Landau-Zener transition in atomic, molecular and optical physics, the band…

Each scheme of state reconstruction comes down to parametrize the state of a quantum system by expectation values or probabilities directly measurable in an experiment. It is argued that the time evolution of these quantities provides an…

Each semigroup describing the time evolution of an open quantum system on a finite dimensional Hilbert space is related to a special structure of this space. It is shown how the space can be decomposed into subspaces: One is related to…

We have shown that DeWitt constraint H=0 on the physical states of the Universe does not prevent Heisenberg operators and its mean values to evolve with time. Mean value from observable, which is singular in classical theory, is also…

The Rigged Hilbert Space (RHS) theory of resonance scattering and decay is reviewed and contrasted with the standard Hilbert space (HS) theory of quantum mechanics. The main difference is in the choice of boundary conditions. Whereas the…

A quantum system S undergoing continuous time measurement is usually described by a jump-diffusion stochastic differential equation. Such an equation is called a stochastic master equation and its solution is called a quantum trajectory.…