Related papers: One qubit almost completely reveals the dynamics o…
For a free falling particle moving in a media which has quadratic velocity force effect on the particle, two equivalent constants of motion, with units of energy, two Lagrangians, and two Hamiltonians are deduced. These quantities describe…
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…
If the block universe view is correct, the future and the past have similar status and one would expect physical theories to involve final as well as initial boundary conditions. A plausible consistency condition between the initial and…
It is argued that the dynamics of an isolated system, due to the concrete procedure by which it is separated from the environment, has a non-Hamiltonian contribution. By a unified quantum field theoretical treatment of typical subdynamics,…
In quantum physics, measurements give random results and yield a corresponding random back action on the state of the system subject to measurement. If a quantum system is probed continuously over time, its state evolves along a stochastic…
This paper investigates the relationship between subsystems and time in a closed nonrelativistic system of interacting bosons and fermions. It is possible to write any state vector in such a system as an unentangled tensor product of…
The interaction between two parts in a compound quantum system may be reconsidered more completely than before and some new understandings and conclusions different from current quantum mechanics are obtained, including the conservation law…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
A general quantum adiabatic theorem with and without the time-dependent orthogonalization is proven, which can be applied to understand the origin of activation energies in chemical reactions. Further proofs are also developed for the…
We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum…
What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? It has been shown that all two-body Hamiltonian evolutions can be simulated using \emph{any} fixed two-body entangling $n$-qubit…
Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
In this work, we develop a mathematical framework to model a quantum system whose Hamiltonian may depend on the state of changing environment, that evolves according to a Markovian process. When the environment changes its state, the…
The short-time behavior of the survival probability of a system governed by a time-dependent non-Hermitian Hamiltonian is derived using to the second order perturbative approach. The resulting expression allows for the analysis of some…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
Simple examples are used to introduce and examine symmetries of open quantum dynamics that can be described by unitary operators. For the Hamiltonian dynamics of an entire closed system, the symmetry takes the expected form which, when the…
Bohmian mechanics is a theory that provides a consistent explanation of quantum phenomena in terms of point particles whose motion is guided by the wave function. In this theory, the state of a system of particles is defined by the actual…
A general dynamical system composed by two coupled sectors is considered. The initial time configuration of one of these sectors is described by a set of classical data while the other is described by standard quantum data. These dynamical…
We consider two models of deterministic active particles in an external potential. In the limit where the speed of a particle is fixed, both models coincide and can be formulated as a Hamiltonian system, but only if the potential is…