Related papers: Critical Missing Equation of Quantum Physics for U…
The textbook treatment in that the wave function of a dynamical system is expanded in an eigenfunction series is investigated. With help of an elementary example and some mathematical theorems, it is revealed that in terms of solving the…
The apparent dichotomy between quantum jumps on the one hand, and continuous time evolution according to wave equations on the other hand, provided a challenge to Bohr's proposal of quantum jumps in atoms. Furthermore, Schroedinger's…
We determine the nature of the QCD transition using lattice calculations for physical quark masses. Susceptibilities are extrapolated to vanishing lattice spacing for three physical volumes, the smallest and largest of which differ by a…
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to…
We found the deviation of the equation of state from ultrarelativistic one due to quantum corrections for a nonequilibrium longitudinally expanding scalar field. Relaxation of highly excited quantum field is usually described in terms of…
In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical…
For a quantum system to be captured by a stationary statistical ensemble, as is common in thermodynamics and statistical mechanics, it is necessary that it reaches some apparently stationary state in the first place. In this book chapter,…
The essentials of quantum theory, the Schr\"odinger equation and the Planck constant, are derived using classical statistical mechanics within the non-local Machan model. The appearance of complex wave function is connected with the…
With a choice of boundary conditions for solutions of the Schr\"odinger equation, state vectors and density operators even for closed systems evolve asymmetrically in time. For open systems, standard quantum mechanics consequently predicts…
Scaling arguments imply that quantum critical points exhibit universal non-linear responses to external probes. We investigate the origins of such non-linearities in transport, which is especially problematic since the system is necessarily…
In quantum mechanical experiments one distinguishes between the state of an experimental system and an observable measured in it. Heuristically, the distinction between states and observables is also suggested in scattering theory or when…
A nonperturbative procedure of solving the time-dependent Schr\"odinger equation, called the multi-projection approach or phase dynamics of quantum mechanics, is derived and illustrated. In addition to introducing a method with that…
Information-theoretic arguments are used to obtain a link between the accurate linearity of Schrodinger's equation and Lorentz invariance: A possible violation of the latter at short distances would imply the appearance of nonlinear…
A nonlinear theory of quantum Brownian motion in classical environment is developed based on a thermodynamically enhanced nonlinear Schrodinger equation. The latter is transformed via the Madelung transformation into a nonlinear quantum…
Quantum criticality is the intriguing possibility offered by the laws of quantum mechanics when the wave function of a many-particle physical system is forced to evolve continuously between two distinct, competing ground states. This…
We explore set-stabilizability by constrained controls, and both controllability and stabilizability can be regarded as the special case of set-stabilizability. We not only clarify how to define an equilibrium point of Schr$\ddot{o}$dinger…
Schr\"{o}dinger's famous Gedankenexperiment involving a cat is used as a motivation to discuss the evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently.…
The momentum representation is seldom used in quantum mechanics courses. Some students are thence surprised by the change in viewpoint when, in doing advanced work, they have to use the momentum rather than the coordinate representation. In…
We study the stability of the Schr\"odinger equation generated by time-dependent Hamiltonians with constant form domain. That is, we bound the difference between solutions of the Schr\"odinger equation by the difference of their…
We investigate the equilibration of an isolated macroscopic quantum system in the sense that deviations from a steady state become unmeasurably small for the overwhelming majority of times within any sufficiently large time interval. The…