相关论文: On quantum evolution as a parallel transport

Geometrically, quantum mechanics is defined by a complex line bundle $L_\hbar$ over the classical particle phase space $T^*{R}^3\cong{R}^6$ with coordinates $x^a$ and momenta $p_a$, $a,...=1,2,3$. This quantum bundle $L_\hbar$ is endowed…

For many quantum models an apparent non-Hermiticity of observables corresponds to their hidden Hermiticity in another, physical Hilbert space. For these models we show that the existence of observables which are manifestly time-dependent…

Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the…

It is remarkable that Heisenberg's position-momentum uncertainty relation leads to the existence of a maximal acceleration for a physical particle in the context of a geometric reformulation of quantum mechanics. It is also known that the…

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…

A fundamental aspect of the quantum-to-classical limit is the transition from a non-commutative algebra of observables to commutative one. However, this transition is not possible if we only consider unitary evolutions. One way to describe…

We present a nonperturbative, first-principles numerical approach for time-dependent problems in the framework of quantum field theory. In this approach the time evolution of quantum field systems is treated in real time and at the…

We argue that the problem of time is not a crucial issue inherent in the quantum picture of the universe evolution. On the minisuperspace model example with the massless scalar field, we demonstrate four approaches to the description of…

We study the Hilbert bundle description of stochastic quantum mechanics in curved spacetime developed by Prugove\v{c}ki, which gives a powerful new framework for exploring the quantum mechanical propagation of states in curved spacetime. We…

We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…

The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained…

We introduce a nonperturbative, first-principles approach to time-dependent problems in quantum field theory. In this approach, the time-evolution of quantum field configurations is calculated in real time and at the amplitude level. This…

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…

It is described a nonlocal interaction between entangled quantum objects, which is initiated by a process different from the reduction of the wave function. The scheme of an experiment realizing a deterministic nonlocal quantum evolution is…

We reexamine the relationship between the path integral and canonical formulation of quantum general relativity. In particular, we present a formal derivation of the Wheeler-DeWitt equation from the path integral for quantum general…

We investigate gravity as a gauge theory in the language of fiber bundles with tools from algebraic geometry. Compelled by the construction of the Eilenberg-MacLane classifying space via Fox derivations in an integral group ring, the origin…

For classical canonical transformations, one can, using the Wigner transformation, pass from their representation in Hilbert space to a kernel in phase space. In this paper it will be discussed how the time-dependence of the uncertainties…

We propose to use the effect of measurements instead of their number to study the time evolution of quantum systems under monitoring. This time redefinition acts like a microscope which blows up the inner details of seemingly instantaneous…

A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…

Quantum cosmology describes universe as a relativistic object with an evolution defined by an equation for the energy density corresponding to the least action principle: (Taganov, 2008). In quantum cosmology this equation plays the same…