arXiv subjects

Janos Polonyi

Publications and source records attributed to Janos Polonyi.

At least 19 recordsLinked to original sources

arXiv2024

Action for classical, quantum, closed and open systems

It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics, respectively. These schemes are based on an unusual feature, a formal redoubling of the degrees of freedom. Several arguments to motivate the redoubling are put forward in classical and quantum mechanics to demonstrate that such a formalism is natural.

quant-ph↗

arXiv2023

Quantum phenomena inside a black hole: quantization of the scalar field iniside horizon in Schwarzschild spacetime

We discuss the problem of the quantization and dynamic evolution of a scalar free field in the interior of a Schwarzschild black hole. A unitary approach to the dynamics of the quantized field is proposed: a time-dependent Hamiltonian governing the Heisenberg equations is derived. It is found that the system is represented by a set of harmonic oscillators coupled via terms corresponding to the creation and annihilation of pairs of particles and that the symmetry properties of the spacetime, homogeneity and isotropy are obeyed by the coupling terms in the Hamiltonian. It is shown that Heisenberg equations for annihilation and creation operators are transformed into ordinary differential equations for appropriate Bogolyubov coefficients. Such a formulation leads to a general question concerning the possibility of gravitationally driven instability, that is however excluded in this case.

gr-qc↗

arXiv2023

Electric current in a translation invariant environment

The master equation for the reduced density matrix of a charged particle interacting with a translation invariant weakly coupled environment is considered. The electric current is renormalized by the system-environment interaction, leading to a direct signature of the environment in the bremsstrahlung. The general solution is given in the absence of the external electromagnetic field and the spread and the decoherence of a wave packet are followed. The increased complexity and importance of the boundary conditions for the density matrix are pointed out.

quant-ph↗

arXiv2022

Symmetry restoration, Tunnelling and the Null Energy Condition

A finite volume allows tunnelling between degenerate vacua in Quantum Field Theory, and leads to remarkable energetic features, arising from the competition of different saddle points in the partition function. We describe this competition for finite temperature at equilibrium, taking into account both static and (Euclidean) time-dependent saddle points. The effective theory for the homogeneous order parameter yields a non-extensive vacuum energy at low temperatures, implying a dynamical violation of the Null Energy Condition.

hep-th↗

arXiv2021

Macroscopic limit of quantum systems

Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the time-dependent expectation value of the coordinate. The emergence of the classical trajectory can be followed for the average of an observable over a large set of independent microscopical systems, and the deterministic classical laws can be recovered in all practical purposes, owing to the largeness of Avogadro's number. This result refers to the observed system without considering the measuring apparatus. The emergence of a classical trajectory is followed qualitatively in Wilson's cloud chamber.

quant-ph↗

arXiv2021

Elementary open quantum states

It is shown that the mixed states of a closed dynamics support a reduplicated symmetry, which is reduced back to the subgroup of the original symmetry group when the dynamics is open. The elementary components of the open dynamics are defined as operators of the Liouville space in the irreducible representations of the symmetry of the open system. These are tensor operators in the case of rotational symmetry. The case of translation symmetry is discussed in more detail for harmonic systems.

quant-ph↗

arXiv2021

Tunnelling and dynamical violation of the Null Energy Condition

The Null Energy Condition is considered the most fundamental of the energy conditions, on which several key results, such as the singularity theorems, are based. The Casimir effect is one of the rare equilibrium mechanisms by which it is breached without invoking modified gravity or non-minimal couplings to exotic matter. In this work we propose an independent dynamical mechanism by which it is violated, with the only ingredients being standard (but non-perturbative) QFT and a minimally coupled scalar field in a double-well potential. As for the Casimir effect, we explain why the Averaged Null Energy Condition should not be violated by this mechanism. Nevertheless, the transient behaviour could have profound impacts in Early Universe Cosmology.

hep-th↗

arXiv2020

Equilibrium properties and decoherence of an open harmonic oscillator

The equilibrium properties of an open harmonic oscillator are considered in three steps: First the creation and destruction operators are generalized for open dynamics and the creation operator is used to construct coherent states. The second step consists of the introduction of the Heisenberg representation where the dynamical decoherence can be identified without making reference to the state of the system. Finally it is pointed out that the quantum fluctuations generate non-continuous limit for infinitesimal system-environment interactions and at the border of the under- and over-damped oscillator.

quant-ph↗

arXiv2019

The Abraham-Lorentz force and electrodynamics at the classical electron radius

The Abraham-Lorentz force is a finite remnant of the UV singular structure of the self interaction of a point charge with its own field. The satisfactory description of such interaction needs a relativistic regulator. This turns out to be a problematic point because the energy of regulated relativistic cutoff theories is unbounded from below. However one can construct point splitting regulators which keep the Abraham-Lorentz force stable. The classical language can be reconciled with QED by pointing out that the effective quantum theory for the electric charge supports a saddle point producing the classical radiation reaction forces.

hep-th↗

arXiv2018

Boost invariant regulator for field theories

It is shown that by imposing the relativistic symmetries on the cutoff in field theories one rules out all known non-perturbative regulators except the point splitting. The relativistic cutoff dynamics is non-local in time and thereby unstable, bringing the very existence of relativistic field theory into question. It is argued within the context of a scalar field theory model that the combination of the point splitting with a sufficiently fast suppression in the field amplitude may lead to stable semiclassical dynamics and to a new kind of realistic vacuum structure.

hep-th↗

arXiv2018

Instantaneous and dynamical decoherence

Two manifestations of decoherence, called instantaneous and dynamical, are investigated. The former reflects the suppression of the interference between the components of the current state while the latter reflects that within the initial state. These types of decoherence are computed in the case of the Brownian motion and the harmonic and anharmonic oscillators within the semiclassical approximation. A remarkable phenomenon, namely the opposite orientation of the time arrow of the dynamical variables compared to that of the quantum fluctuations generates a double exponential time dependence of the dynamical decoherence in the presence of a harmonic force. For the weakly anharmonic oscillator the dynamical decoherence is found to depend in a singular way on the amount of the anharmonicity.

quant-ph↗

arXiv2018

Stability and causality of multi-local theories

The regularized theories are non-local at the scale of the cutoff, leading so to the usual difficulties of non-local theories. In this work the conservation laws and causality are investigated for classical field theories with multi-cluster action. The conservation laws are found to play a less significant role than in local theories because due to the non-locality the conserved quantities are not integrals of the motion, and they can exist even without underlying symmetries. Moreover, the conservation of the energy can not prevent instability brought about by the unbounded nature of the energy from below. Hence a sufficient condition of stability is lost. Theories, obtained by appropriate point splitting of local interactions are shown to be causal thereby a necessary condition of stability can be retained.

hep-th↗

arXiv2017

Time scale of stationary decoherence

The decoherence of a test particle interacting with an ideal gas is studied by the help of the effective Lagrangian, derived in the leading order of the perturbation expansion and in order $\ord{\partial^2_t}$. The stationary decoherence time is found to be comparable to or longer than the diffusion time. The decoherence time reaches its minimal value for classical, completely decohered environment, suggesting that physical decoherence is slowed down as compared with diffusion by the quantum coherence of the environment.

quant-ph↗

arXiv2016

Spontaneous breakdown of the time reversal symmetry

The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized $ε$-prescription where the non-uniform convergence of the limit $ε\to0$ leaves behind a spontaneous breakdown of the time reversal symmetry.

cond-mat.stat-mech↗

arXiv2015

Dissipation and decoherence by ideal quantum gas

The effective Lagrangian of a test particle, interacting with an ideal gas, is calculated with in the closed time path formalism in the one-loop and the leading order of the particle trajectory. The expansion in the time derivative is available for slow enough motion and it uncovers diffusive effective forces and decoherence for the coordinate and the momentum. A pure Newtonian friction force and an anisotrop coordinate decoherence are found for zero temperature ideal gas of fermions.

cond-mat.stat-mech↗

arXiv2015

A Gaussian density matrix under decoherence and friction

The time evolution of a Gaussian density matrix of a one dimensional particle, generated by a quadratic, ${\cal O}(\partial_t^2)$ effective Lagrangian, describing a harmonic potential, a friction force and decoherence, is studied within the Closed Time Path formalism. The density matrix converges to an asymptotic form, given by a completely decohered thermal state with an ${\cal O}(\hbar)$ temperature in the translation invariant case. The time evolution of the state of a harmonic oscillator is followed numerically. The asymptotic density matrix, the fixed point of the master equation, is found analytically and its dependence on the oscillator frequency, the friction constant and the decoherence strength is explored.

cond-mat.stat-mech↗

arXiv2015

Dynamics of the electric current in an ideal electron gas: a sound mode inside the quasi-particles

We study the equation of motion for the Noether current in an electron gas within the framework of the Schwinger-Keldysh Closed-Time-Path formalism. The equation is shown to be highly non-linear and irreversible even for a non-interacting, ideal gas of electrons at non-zero density. We truncate the linearised equation of motion, written as the Laurent series in Fourier space, so that the resulting expressions are local in time, both at zero and at small finite temperatures. Furthermore, we show that the one-loop Coulomb interactions only alter the physical picture quantitatively, while preserving the characteristics of the dynamics that the electric current exhibits in the absence of interactions. As a result of the composite nature of the Noether current, {\it composite sound} waves are found to be the dominant IR collective excitations at length scales between the inverse Fermi momentum and the mean free path that would exist in an interacting electron gas. We also discuss the difference and the transition between the hydrodynamical regime of an ideal gas, defined in this work, and the hydrodynamical regime in phenomenological hydrodynamics, which is normally used for the description of interacting gases.

hep-th↗

arXiv2015

Viscosity and dissipative hydrodynamics from effective field theory

With the goal of deriving dissipative hydrodynamics from an action, we study classical actions for open systems, which follow from the generic structure of effective actions in the Schwinger-Keldysh Closed-Time-Path formalism with two time axes and a doubling of degrees of freedom. The central structural feature of such effective actions is the coupling between degrees of freedom on the two time axes. This reflects the fact that from an effective field theory point of view, dissipation is the loss of energy of the low-energy hydrodynamical degrees of freedom to the integrated-out, UV degrees of freedom of the environment. The dynamics of only the hydrodynamical modes may therefore not posses a conserved stress-energy tensor. After a general discussion of the CTP effective actions, we use the variational principle to derive the energy-momentum balance equation for a dissipative fluid from an effective Goldstone action of the long-range hydrodynamical modes. Despite the absence of conserved energy and momentum, we show that we can construct the first-order dissipative stress-energy tensor and derive the Navier-Stokes equations near hydrodynamical equilibrium. The shear viscosity is shown to vanish in the classical theory under consideration, while the bulk viscosity is determined by the form of the effective action. We also discuss the thermodynamics of the system and analyse the entropy production.

hep-th↗