The space-time structure of quantum systems in external fields

Vito Luigi Lepore

Tejinder P. Singh

Collapse models possibly suggest the need for a better understanding of the structure of space-time. We argue that physical space, and space-time, are emergent features of the Universe, which arise as a result of dynamical collapse of the wave function. The starting point for this argument is the observation that classical time is external to quantum theory, and there ought to exist an equivalent reformulation which does not refer to classical time. We propose such a reformulation, based on a non-commutative special relativity. In the spirit of Trace Dynamics, the reformulation is arrived at, as a statistical thermodynamics of an underlying classical dynamics in which matter and non-commuting space-time degrees of freedom are matrices obeying arbitrary commutation relations. Inevitable statistical fluctuations around equilibrium can explain the emergence of classical matter fields and classical space-time, in the limit in which the universe is dominated by macroscopic objects. The underlying non-commutative structure of space-time also helps understand better the peculiar nature of quantum non-locality, where the effect of wave-function collapse in entangled systems is felt across space-like separations.

Siamak Khademi, S. Nasiri, Seyed Majid Saberi Fathi +1 more

Recently, it is shown that the extended phase space formulation of quantum mechanics is a suitable technique for studying the quantum dissipative system. Here, as an application of this formalism, we consider a dissipative system of charged particles interacting with an external time dependent electric field. Such a system has been investigating by Buch and Denman, and two solutions with completely different structure have been obtained for Schrödinger's equation in two different gauges. We demonstrate how both gauges lead to the same conductivity by generalizing the gauge transformations to the phase space and using the extended phase space technique.

Klaus Fredenhagen

Sumiyoshi Abe

The problem of extracting the work from a quantum-thermodynamic system driven by slowly varying external parameters is discussed. It is shown that there naturally emerges a gauge-theoretic structure. The field strength identically vanishes if the system is in an equilibrium state, i.e., the nonvanishing field strength implies that the system is in a nonequilibrium quasi-stationary state. The work done through a cyclic process in the parameter space is given in terms of the flux of the field. This general formalism is applied to an example of a single spin in a varying magnetic field, and the maximum power output is discussed in a given finite-time cyclic process.

Tim Maudlin