Using the Zubarev quantum-statistical density operator, we calculated the corrections to the energy-momentum tensor of a massless fermion gas associated with acceleration. It is shown that when fourth-order corrections are taken into account, the energy-momentum tensor in the laboratory frame is equal to zero at a proper temperature measured by a comoving observer equal to Unruh temperature. Consequently, the Minkowski vacuum is visible to the accelerated observer as a medium filled with a heat bath of particles with the Unruh temperature, which is the essence of the Unruh effect.
The relativistic form of the Zubarev density operator can be used to study quantum effects associated with acceleration of the medium. In particular, it was recently shown that the calculation of perturbative corrections in acceleration based on the Zubarev density operator makes it possible to show the existence of Unruh effect. In this paper, we present the details of the calculation of quantum correlators arising in the fourth order of the perturbation theory needed to demonstrate the Unruh effect. Expressions for the quantum corrections for massive fermions are also obtained.
The Unruh effect has been investigated from the point of view of the quantum statistical Zubarev density operator in space with the Minkowski metric. Quantum corrections of the fourth order in acceleration to the energy-momentum tensor of real and complex scalar fields, and Dirac field are calculated. Both massless and massive fields are considered. The method for regularization of discovered infrared divergences for scalar fields is proposed. The calculated corrections make it possible to substantiate the Unruh effect from the point of view of the statistical approach, and to explicitly show …
We demonstrate that the energy density of an accelerated fermion gas evaluated within quantum statistical approach in Minkowski space is related to a quantum correction to the vacuum expectation value of the energy-momentum tensor in a space with non-trivial metric and conical singularity. The key element of the derivation is the existence of a novel class of polynomial Sommerfeld integrals. The emerging duality of quantum statistical and geometrical approaches is explicitly checked at temperatures $T$ above or equal to the Unruh temperature $T_U$. Treating the acceleration as an imaginary par…
The thermal spectrum seen by accelerated observers in Minkowski space - known as the Unruh effect - is derived within the tunneling mechanism. This is a new result in this mechanism and it completes the treatment of Unruh effect via tunneling. Both Bose-Einstein and Fermi-Dirac spectrum is derived by considering tunneling of scalar and spin half particles respectively, across the accelerated Rindler horizon. Full solutions of Klein-Gordon and Dirac equations in the Rindler metric are employed to achieve this, instead of approximate solutions.
We have investigated the Unruh effect in Anti de-Sitter (AdS) spacetime by examining the response function of an Unruh-DeWitt particle detector with uniform constant acceleration. An exact expression of the detector response function for the scalar field has been obtained with different levels of non-linearity in even dimensional AdS spacetime. We also showed how the response of the accelerated Unruh detector coupled quadratically to massless Dirac field in $D$ dimensional $(D \geq 2)$ AdS spacetime is proportional to that of a detector linearly coupled to a massless scalar field in $2D$ dimen…
Since quantum field theories do not possess proper position observables, Unruh-DeWitt detector models serve as a key theoretical tool for extracting localized spatio-temporal information from quantum fields. Most studies have been limited, however, to Unruh-DeWitt (UDW) detectors that are coupled linearly to a scalar bosonic field. Here, we investigate UDW detector models that probe fermionic as well as bosonic fields through both linear and quadratic couplings. In particular, we present a renormalization method that cures persistent divergencies of prior models. We then show how perturbative …
We examine an Unruh-DeWitt particle detector which couples linearly to the scalar density of a massless Dirac field on the static cylindrical quotient of the (1+1)-dimensional Minkowski spacetime, allowing the detector's motion to remain arbitrary and working to leading order in perturbation theory. We show that the detector's response distinguishes the periodic and antiperiodic spin structures, and the zero mode that is present for periodic spinors contributes to the response by a state-dependent but well defined and controllable amount.
We give a rigorous definition of the Unruh state in the setting of massless Dirac fields on slowly rotating Kerr spacetimes. In the black hole exterior region, we show that it is asymptotically thermal at Hawking temperature on the past event horizon. Furthermore, we demonstrate that in the union of the exterior and interior regions, the Unruh state is pure and Hadamard. The main ingredients are the Häfner-Nicolas scattering theory, new microlocal estimates for characteristic Cauchy problems and criteria on the level of square-integrable solutions.
It is well known that a receding mirror in Minkowski spacetime can model the formation of a black hole, producing Hawking-like radiation at late times. We ask what an observer would need to do to discern whether the radiation is fermionic or bosonic. Specialising to massless fields in 1+1 dimensions, we find that an Unruh-DeWitt detector accomplishes this: the late time transition rate of a detector coupled linearly to the scalar density of a spinor field is proportional to the Helmholtz free energy density of a fermionic thermal bath, hence showing a clear sign of Fermi-Dirac statistics, with…
We examine an Unruh-DeWitt particle detector that is coupled linearly to the scalar density of a massless Dirac field in Minkowski spacetimes of dimension $d\ge2$ and on the static Minkowski cylinder in spacetime dimension two, allowing the detector's motion to remain arbitrary and working to leading order in perturbation theory. In $d$-dimensional Minkowski, with the field in the usual Fock vacuum, we show that the detector's response is identical to that of a detector coupled linearly to a massless scalar field in $2d$-dimensional Minkowski. In the special case of uniform linear acceleration…
We study the evolution of neutrinos in a background matter moving with a linear acceleration. The Dirac equation for a massive neutrino electroweakly interacting with background fermions is obtained in a comoving frame where matter is at rest. We solve this Dirac equation for ultrarelativistic neutrinos. The neutrino quantum states in matter moving with a linear acceleration are obtained. We demonstrate that the neutrino electroweak interaction with an accelerated matter leads to the vacuum instability which results in the neutrino-antineutrino pairs creation. We rederive the temperature of th…
The Unruh effect is a quantum relativistic effect where the accelerated observer perceives the vacuum as a thermal state. Here we propose the experimental realization of the Unruh effect for interacting ultracold fermions in optical lattices by a sudden quench resulting in vacuum acceleration with varying interactions strengths in the real temperature background. We observe the inversion of statistics for the low lying excitations in the Wightman function as a result of competition between the spacetime and BCS Bogoliubov transformations. This paper opens up new perspectives for simulators of …
Total entropy generated by the Unruh effect is calculated within the framework of information theory. In contrast to previous studies, here the calculations are done for the finite time of existence of the non-inertial reference frame. In this case only the finite number of particles is produced. Dependence on mass of the emitted particles is taken into account. Analytic expression for the entropy of radiated boson and fermion spectra is derived. We study also its asymptotics corresponding to limiting cases of low and high acceleration. The obtained results can be further generalized to other …
The relative entropy between very high energy localized excitations and the vacuum, where both states are reduced to a spatial region, gives place to a precise definition of a local temperature produced by vacuum entanglement across the boundary. This generalizes the Unruh temperature of the Rindler wedge to arbitrary regions. The local temperatures can be read off from the short distance leading terms in the modular Hamiltonian. For free scalar and fermion fields they have a universal geometric expression that follows by solving a particular eikonal type equation in Euclidean space. This equa…
We analyse the energy cost of building or demolishing a wall for a massless Dirac field in (1+1)-dimensional Minkowski spacetime and the response of an Unruh-DeWitt particle detector to the generated radiation. For any smoothly-evolving wall, both the field's energy density and the detector's response are finite. In the limit of rapid wall creation or demolition, the energy density displays a delta function squared divergence. By contrast, the response of an Unruh-DeWitt detector, evaluated within first-order perturbation theory, diverges only logarithmically in the duration of the wall evolut…
Ultracold fermionic atoms in an optical lattice, with a sudden position-dependent change (a quench) in the effective dispersion relation, have been proposed by Rodríguez-Laguna et al. as an analogue spacetime test of the Unruh effect. We provide new support for this analogue by analysing a massless scalar field on a $(1+1)$-dimensional continuum spacetime with a similar quench: an early time Minkowski region is joined at a constant time surface, representing the quench, to a late time static region in which left and right asymptotically Rindler domains are connected by a smooth negative curvat…
The present thesis aimed to examine the effects of vorticity on the thermodynamics of relativistic quantum systems. We extend the Zubarev's non-equilibrium statistical operator method to address quantum effects induced by vorticity in the presence of chiral matter and external electromagnetic field and keeping full covariant and quantum properties of the system. To investigate the effects of vorticity, this work has been focused on systems consisting of massless chiral fermions. We recovered the significant quantum phenomena known in the literature, namely the chiral magnetic effect, the chira…
We consider an Unruh-DeWitt detector interacting with a massless Dirac field. Assuming that the detector is moving along an hyperbolic trajectory, we modeled the effects of fluctuations in the event horizon using a Dirac equation with random coefficients. First, we develop the perturbation theory for the fermionic field in a random media. Further we evaluate corrections due to the randomness in the response function associated to different model detectors.
This article investigates the Schwinger effect for fermions with background electric and magnetic fields of constant strengths from the point of view of a uniformly accelerated or the Rindler observer. The Dirac equation is solved in a closed form, and the field quantisation in the $(3+1)$-dimensional Rindler spacetime is performed. The orthonormal local in and out modes for the causally disconnected right and left wedges and the Bogoliubov relations between them are obtained. Next, the global modes are constructed to cover the whole spacetime, and the Bogoliubov relationship between the local…
We study some aspects of gravity in relation to flat spacetime. At first, we study an accelerated observer in Minkowski space as a quantum tunnelling problem in Rindler space. Both Bosonic and Fermionic modes are calculated to construct a reduced density matrix of particles tunnelling out across the accelerated Rindler horizon, giving a thermal spectrum characterized by a temperature proportional to the local acceleration - Unruh temperature. So, we calculate both the spectrum and temperature from within the tunnelling framework. In another direction, following Utiyama-Sciama-Kibble, we locali…
