Finite time measurements by Unruh–DeWitt detector and Landauer’s principle

Abstract

The model of Unruh-DeWitt detector coupled to the scalar field for finite time is studied. A systematic way of computing finite time corrections in various cases is suggested and nonperturbative effects like thermalization are discussed. It is shown in particular that adiabatic switching off the coupling between the detector and the thermal bath leaves non-vanishing corrections to the detector's levels distribution. Considering the two level detector as an information bearing degree of freedom encoding one bit of information, limits on external work for the detector's (de)couling in finite time following from the Landauer's bound are formulated.1 In abelian vector field theory, for example, instead of integration over vector field DA µ one can equivalently integrate over tensor fields with the Bianchi identities constraint DF µν δ(∂F ). The standard F 2 -action contains derivatives and describes propagation for the former measure but is trivial Gaussian local one with the latter measure. 1 QED. Renormalizability, however, does not mean naturalness. Computing, for example, average of some local d-dimensional operator T [φ] in a theory with UV cutoff Λ, one gets typically (up to, perhaps, logarithms):The first term characterizes ad hoc assumptions about the integration measure/detector (for example, geometry of the lattice with the link size a ∼ 1/Λ used for computation), but not the genuine physics of this operator. Of course in many cases symmetries of the theory guarantee c = 0, but if not, we have to work out a way of disentangling "the physics of the detector" from "the physics of the physics" (which presumably is hidden in the finite part). Notable examples include vacuum energy density, Higgs boson mass and gluon condensate, where only in the latter case the answer is known (qualitatively, but not quantitatively) -quantum scale anomaly of Yang-Mills theory and dimensional transmutation take care of unphysical UV scale Λ to become physical scale Λ QCD . In other cases of this sort, like cosmological constant problem or hierarchy problem a solution is yet to be found. But in most cases in particle physics we assume that dynamics, described by the action is uncorrelated with dynamics of the measure and for good reasons: typical scale of the former is given by strong interaction distance of ∼ 10 −15 meters and even smaller for weak interactions, while detectors are macroscopic objects having sizes of the order of dozens of microns and larger. All the standard perturbative quantum field theory machinery (asymptotic states; propagators computed in plane waves basis etc.) is based on this assumption. Even if the detector dynamics is relevant, like in case of Unruh effect and similar phenomena -one usually tries to disentangle "beautiful" field theoretic part (universal response functions etc) from "ugly" detector part (concrete models of the detector). On the other hand, to what extent it is possible is undoubtedly quantitative question which should be analyzed in each particular problem.The measurement problem has...

Unruh effect for detectors in superposition of accelerations

“…When considering switching functions in the interaction, the switching on and off process can itself excite the detector, this effect getting scrambled with the excitations due to the Unruh effect in a way which does not always allow for a clear separation [27,28,29]. In order to avoid this situation, we need to consider smooth switching functions with an interaction time much larger than the inverse of the minimum frequency ω 1 that we wish to explore.…”

Quantum Measurements in a Finite Space–Time Domain

“…There is no reason why τ e f f should coincide in a parametric sense with τ m in the general case. The universal character of 1/τ 2 e f f asymptotic Equation (17) could well mean actual 1/τ m (and not naively expected 1/τ 2 m ) dependence for the leading finite time correction; see concrete examples in Reference [4]. This means that correction to the leading perturbative answer for the transition probability in time τ m could be constant (not decreasing with rise of τ m ).…”

“…so that p(t) = (1 + e βΩ ) −1 , which is nothing but the Boltzmann distribution, as it should be. In the nonstationary case the result is given by (see details in Reference [4]):…”

“…In a Markovian approximation, the probability evolution with time can be approximated by the following equation (see Reference [4] for details):…”

“…In this contribution, we present the main results of the formalism [4] for systematic studies of the UDW detector interacting with the field bath for a finite proper time. Various aspects of this problem were discussed in the literature [5][6][7][8][9][10][11], and our work [4] is based on these findings.…”