Related papers: A Noether Theorem for Markov Processes
We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by…
The relational approach to quantum states asserts that the physical description of quantum systems is always relative to something or someone. In relational quantum mechanics (RQM) it is relative to other quantum systems, in the…
In the paper we prove that a quadratic stochastic process satisfies the ergodic principle if and only if the associated Markov process satisfies one.
We provide the quantum mechanics of many particles moving in twisted N-enlarged Newton-Hooke space-time. In particular, we consider the example of such noncommutative system - the set of M particles moving in Coulomb field of external…
From molecular machines to quantum dots, a wide range of mesoscopic systems can be modeled by periodically driven Markov processes, or stochastic pumps. Currents in the stochastic pumps are delimited by an exact no-go condition called the…
We extend Noether's symmetry theorem to fractional action-like variational problems with higher-order derivatives.
We present a new theorem describing stable solutions for a driven quantum system. The theorem, coined `inertial theorem', is applicable for fast driving, provided the acceleration rate is small. The theorem states that in the inertial limit…
We investigate two interacting open quantum systems whose time evolutions are governed by Markovian master equations. We show a class of coupled systems whose interaction leaves invariant the steady state of one of the systems, i.e., only…
The first part of this paper develops a geometric setting for differential-difference equations that resolves an open question about the extent to which continuous symmetries can depend on discrete independent variables. For general…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
Noether symmetry for higher order gravity theory has been explored, with the introduction of an auxiliary variable which gives the only correct quantum desccription of the theory, as shown in a series of earlier papers. The application of…
A slight modification of one axiom of quantum theory changes a reversible theory into a time asymmetric theory. Whereas the standard Hilbert space axiom does not distinguish mathematically between the space of states (in-states of…
A non-commuting measurement transfers, via the apparatus, information encoded in a system's state to the external "observer". Classical measurements determine properties of physical objects. In the quantum realm, the very same notion…
This chapter reviews an information theoretic approach to deriving quantum fluctuation theorems. When a thermal system is driven from equilibrium, random quantities of work are required or produced: the Crooks equality is a classical…
Decoherence in Markovian systems can result indirectly from the action of a system Hamiltonian which is usually fixed and unavoidable. Here, we show that in general in Markovian systems, because of the system Hamiltonian, quantum…
It is shown that quantum-type coherence, leading to indeterminism and interference of probabilities, may in principle exist in the absence of the Planck constant and a Hamiltonian. Such coherence is a combined effect of a symmetry (not…
We investigate what can be concluded about a quantum system when sequential quantum measurements of its observable -- a prominent example of the so-called quantum stochastic process -- fulfill the Kolmogorov consistency condition and thus…
In this paper we study the infinitesimal symmetries, Newtonoid vector fields, infinitesimal Noether symmetries and conservation laws of Hamiltonian systems. Using the dynamical covariant derivative and Jacobi endomorphism on the cotangent…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
The problem of time is a deep paradox in our physical description of the world. According to Aristotle's relational theory, time is a measure of change and does not exist on its own. In contrast, quantum mechanics, just like Newtonian…