Related papers: Quantum mechanics with time-dependent parameters
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and…
Time-dependent quantum evolution is described by an algebraic connection on a $C^\infty(R)$-module of sections of a $C^*$-algebra (or Hilbert) fibre bundle.
Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes…
For time-dependent systems the wavefunction depends explicitly on time and it is not a pure state of the Hamiltonian. We construct operators for which the above wavefunction is a pure state. The method is based on the introduction of…
We present a reformulation of quantum adiabatic theory in terms of an emergent electromagnetic framework, emphasizing the physical consequences of geometric structures in parameter space. Contrary to conventional approaches, we demonstrate…
We present a unified view of the Berry phase of a quantum system and its entanglement with surroundings. The former reflects the nonseparability between a system and a classical environment as the latter for a quantum environment, and the…
When there is a family of complex structures on the phase space, parametrized by a set $S$, the prequantum Hilbert spaces produced by geometric quantization, using the half-form correction, also depends on these parameters. This way we…
Some elements of classical mechanics and classical statistical mechanics are formulated in terms of fibre bundles. In the bundle approach the dynamical and distribution functions are replaced by liftings of paths in a suitably chosen…
We propose a new fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in…
We describe the geometric (Berry) phases arising when some quantum systems are driven by control classical parameters but also by outer classical stochastic processes (as for example classical noises). The total geometric phase is then…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed…
We calculate Berry's phase when the driving field, to which a spin-1/2 is coupled adiabatically, rather than the familiar classical magnetic field, is a quantum vector operator, of noncommuting, in general, components, e.g., the angular…
We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous K\"ahler manifolds X=G/H, which can be considered as the phase spaces of classical systems and which are, in…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits…
To enhance the consistency between the quantum descriptions of waves and particles, we quantise mechanical point particles in this paper in the same physically-motivated way as we previously quantised light in quantum electrodynamics…
We define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time-parameter space for a quantum state, by considering small variations in both time and wave function parameters. Compared to the…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…