Unruh Detector Research Articles

Accelerated paths and Unruh effect. Part I. Scalars and fermions in Anti De Sitter spacetime

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 ≥ 2) AdS spacetime is proportional to that of a detector linearly coupled to a massless scalar field in 2D dimensional AdS spacetime. Here, the fermionic and scalar matter field is coupled minimally and conformally to the background AdS metric, respectively. Finally, we discuss about the extension of the results for more general stationary motion.

The Master Equation for Two-Level Accelerated Systems at Finite Temperature

In this work we study the behaviour of two weakly coupled quantum systems, described by a separable density operator; one of them is a single oscillator, representing a microscopic system, while the other is a set of oscillators which perform the role of a \emph{reservoir} in thermal equilibrium. From the Liouville-Von Neumann equation for the reduced density operator, we devise the master equation that governs the evolution of the microscopic system, incorporating the effects of temperature via Thermofield Dynamics formalism by suitably redefining the vacuum of the macroscopic system. As applications, we initially investigate the behaviour of a Fermi oscillator in the presence of a heat bath consisting of a set of Fermi oscillators and that of an atomic two-level system interacting with a scalar radiation field, considered as a \emph{reservoir}, by constructing the corresponding master equation which governs the time evolution of both sub-systems at finite temperature. Finally, we calculate the energy variation rates for the atom and the field, as well as the atomic population levels, both in the inertial case and at constant proper acceleration, considering the two-level system as a prototype of an Unruh detector, for admissible couplings of the radiation field.

Unruh effect without Rindler horizon

We investigate the Unruh effect for a massless scalar field in the two-dimensional Minkowski space in the presence of a uniformly accelerated perfect mirror, with the trajectory of the mirror chosen in such a way that the mirror completely masks the Rindler horizon from the space–time region of interest. We find that the characteristic thermodynamical properties of the effect remain unchanged, i.e. the response of a uniformly co-accelerated Unruh detector and the distribution of the Rindler particles retain their thermal form. However, since in this setup there are no unobserved degrees of freedom of the field, the thermal statistics of the Rindler particles are inconsistent with an initial pure vacuum, which leads us to reconsider the problem for the more physical case when the mirror is inertial in the past. In these conditions we find that the distribution of the Rindler particles is non-thermal even in the limit of infinite acceleration times, but effective thermal statistics can be recovered provided that one is restricted to the expectation values of smeared operators associated with finite norm Rindler states. We explain how the thermal statistics in our problem can be understood in analogy with those in the conventional version of the effect.

On the cancellation mechanism of radiation from the Unruh detector

A uniformly accelerated detector (Unruh detector) in the Minkowski vacuum is excited as if it is exposed to the thermal bath with temperature proportional to its acceleration. In the inertial frame, since both of an excitation and a deexcitation of the detector are accompanied by emission of radiation into the Minkowski vacuum, one may suspect that the Unruh detector emits radiation like the Larmor radiation from an accelerated charged particle. However, it is known that the radiation is miraculously cancelled by a quantum interference effect. In this paper, we investigate under what condition the radiation cancels out. We first show that the cancellation occurs if the Green function satisfies a relation similar to the Kubo-Martin-Schwinger (KMS) condition. We then study two examples, Unruh detectors in the 3+1 dimensional Minkowski spacetime and in the de Sitter spacetime. In both cases, the relation holds only in a restricted region of the spacetime, but the radiation is cancelled in the whole spacetime. Hence the KMS-like relation is necessary but not sufficient for the cancellation to occur.

ON THE UNRUH EFFECT IN DE SITTER SPACE

We give an interpretation of the temperature in de Sitter universe in terms of a dynamical Unruh effect associated with the Hubble sphere. As with the quantum noise perceived by a uniformly accelerated observer in static spacetimes, observers endowed with a proper motion can in principle detect the effect. In particular, we study a "Kodama observer" as a two-field Unruh detector for which we show the effect is approximately thermal. We also estimate the back-reaction of the emitted radiation and find trajectories associated with the Kodama vector field are stable.

Lamb shift of Unruh detector levels

We argue that the energy levels of an Unruh detector experience an effect similar to the Lamb shift in quantum electrodynamics. As a consequence, the spectrum of energy levels in a curved background is different from that in flat space. As examples, we consider a detector in an expanding universe and in Rindler space, and for the latter case we suggest a new expression for the local virtual energy density seen by an accelerated observer. In the ultraviolet domain, that is when the space between the energy levels is larger than the Hubble rate or the acceleration of the detector, the Lamb shift quantitatively dominates over the thermal response rate.

Energy density in expanding universes as seen by an Unruh detector

We consider the response of an Unruh detector to scalar fields in an expanding space-time. When combining transition elements of the scalar field Hamiltonian with the interaction operator of detector and field, one finds at second order in time-dependent perturbation theory a transition amplitude, which actually dominates in the ultraviolet over the first order contribution. In particular, the detector response faithfully reproduces the particle number implied by the stress-energy of a minimally coupled scalar field, which is inversely proportional to the energy of a scalar mode. This finding disagrees with the contention that in de Sitter space, the response of the detector drops exponentially with particle energy and therefore indicates a thermal spectrum.

Unruh response functions for scalar fields in de Sitter space

We calculate the response functions of a freely falling Unruh detector in de Sitter space coupled to scalar fields of different couplings to the curvature, including the minimally coupled massless case. Although the responses differ strongly in the infrared as a consequence of the amplification of superhorizon modes, the energy levels of the detector are thermally populated.

S-brane thermodynamics

The description of string-theoretic s-branes at g_s=0 as exact worldsheet CFTs with a (lambda cosh X^0) or (lambda e^(X^0)) boundary interaction is considered. Due to the imaginary-time periodicity of the interaction under X^0 -> X^0 + 2 pi i, these configurations have intriguing similarities to black hole or de Sitter geometries. For example, the open string pair production as seen by an Unruh detector is thermal at temperature T = 1/4 pi. It is shown that, despite the rapid time dependence of the s-brane, there exists an exactly thermal mixed state of open strings. The corresponding boundary state is constructed for both the bosonic and superstring cases. This state defines a long-distance Euclidean effective field theory whose light modes are confined to the s-brane. At the critical value of the coupling lambda=1/2, the boundary interaction simply generates an SU(2) rotation by pi from Neumman to Dirichlet boundary conditions. The lambda=1/2 s-brane reduces to an array of sD-branes (D-branes with a transverse time dimension) on the imaginary time axis. The long range force between a (bosonic) sD-brane and an ordinary D-brane is shown from the annulus diagram to be 11/12 times the force between two D-branes. The linearized time-dependent RR field F=dC produced by an sD-brane in superstring theory is explicitly computed and found to carry a half unit of s-charge Q_s=\int_S *F=1/2, where S is any transverse spacelike slice.

Can an Unruh Detector Feel a Cosmic String?

Unruh's detector calculation is used to study the effect of the defect angle β in a space-time with a cosmic string for both the excitation and deexcitation cases. It is found that a rotating detector results in a non-zero effect for both finite (small) and infinite (large) time.

Quantum detection on the vacuum by non-uniformly accelerated observers

We consider relativistic quantum detectors moving with a wide class of accelerations on the standard vacuum Minkowski state. The quantum field to be detected induces transitions between two kinds of detector quanta. The detector measures zero, a planckian spectrum or infinity depending on the asymptotic properties of the acceleration. This generalizes Unruh's detector and shows that Rindler's observers are not in this sense, preferred. This throws light on the “relativity” of the concept of vacuum and on the physical interpretation of QFT in accelerated coordinates.