We consider a real massless scalar field inside a cavity with two moving mirrors in a two-dimensional spacetime, satisfying Dirichlet boundary condition at the instantaneous position of the boundaries, for arbitrary and relativistic laws of motion. Considering vacuum as the initial field state, we obtain formulas for the exact value of the energy density of the field and the quantum force acting on the boundaries, which extend results found in previous papers. For the particular cases of a cavity with just one moving boundary, non-relativistic velocities, or in the limit of infinity length of the cavity (a single mirror), our results coincide with those found in the literature.
In a two-dimensional conformal field theory with a moving mirror, known as a moving mirror model, the time evolution of the entanglement entropy shows a Page like curve. This implies that the moving mirror model is useful to understand the island formula. In this paper, we study the time evolution of the subregion CV complexity in the moving mirror model for a better understanding of the island formula of the complexity. In contrast to the entanglement entropy, the subregion CV complexity shows a peculiar behaviour. We discuss this behaviour in more detail.
We study the 2D massive fields in the presence of moving mirrors. We do that for standing mirror and mirror moving with constant velocity. We calculate the modes and commutation relations of the field operator with the corresponding conjugate momentum in each case. We find that in case of the ideal mirror, which reflects modes with all momenta equally well, the commutation relations do not have their canonical form. However, in the case of non-ideal mirror, which is transparent for the modes with high enough momenta, the commutation relations of the field operator and its conjugate momentum ha…
We employ the holographic method to study fluctuations and dissipation of an $n$-dimensional moving mirror coupled to quantum critical theories in $d$ spacetime dimensions. The bulk counterpart of the mirror with perfect reflection is a D$(n+1)$ brane in the Lifshitz geometry of $d+1$ dimensions. The motion of the mirror can be realized from the dynamics of the brane at the boundary of the bulk. The excited modes of the brane in the bulk render the mirror undergoing Brownian motion. For small displacement of the mirror, we derive the analytical results of the correlation functions and response…
The effective strength of EM interactions can be controlled by confining the fields to a cavity and these effects might be used to push graphene into a strongly coupled regime. We study the similar D3/probe D5 system on a compact space and discuss the gravity dual for a cavity between two mirrors. We show that the introduction of a conformal symmetry breaking length scale introduces a mass gap on a single D5 sheet. Bilayer configurations display exciton condensation between the sheets. There is a first order phase transition away from the exciton condensate if a strong enough magnetic field is…
We extend our previous work on the functional approach to the dynamical Casimir effect, to compute dissipative effects due to the relative motion of two flat, parallel, imperfect mirrors in vacuum. The interaction between the internal degrees of freedom of the mirrors and the vacuum field is modeled with a nonlocal term in the vacuum field action. We consider two different situations: either the motion is `normal', i.e., the mirrors advance or recede changing the distance $a(t)$ between them; or it is `parallel', namely, $a$ remains constant, but there is a relative sliding motion of the mirro…
We study photon creation in a cavity with two perfectly conducting moving mirrors. We derive the dynamic equations of the modes and study different situations concerning various movements of the walls, such as translational or breathing modes. We can even apply our approach to one or three dimensional cavities and reobtain well known results of cavities with one moving mirror. We compare the numerical results with analytical predictions and discuss the effects of the intermode coupling in detail as well as the non perturbative regime. We also study the time evolution of the energy density as w…
We consider a movable mirror coupled to a one-dimensional massless scalar field in a cavity. Both the field and the mirror's mechanical degrees of freedom are described quantum-mechanically, and they can interact each other via the radiation pressure operator. We investigate the dynamical evolution of mirror and field starting from a nonequilibrium initial state, and their local interaction which brings the system to a stationary configuration for long times. This allows us to study the time-dependent dressing process of the movable mirror interacting with the field, and its dynamics leading t…
We systematically study moving mirror models in two-dimensional conformal field theory (CFT). By focusing on their late-time behavior, we separate the mirror profiles into four classes, named type A (timelike) mirrors, type B (escaping) mirrors, type C (chasing) mirrors, and type D (terminated) mirrors. We analytically explore the characteristic features of the energy flux and entanglement entropy for each type and work out their physical interpretation. Moreover, we construct their gravity duals for which end-of-the-world (EOW) branes play a crucial role. Depending on the mirror type, the pro…
There is an exact correspondence between the simplest solution to Einstein's equations describing the formation of a black hole and a particular moving mirror trajectory. In both cases the Bogolubov coefficients in 1+1 dimensions are identical and can be computed analytically. Particle creation is investigated by using wave packets. The entire particle creation history is computed, incorporating the early-time non-thermal emission due to the formation of the black hole (or the early-time acceleration of the moving mirror) and the evolution to a Planckian spectrum.
We investigate the dynamical Casimir effect for a one-dimensional resonant cavity, with one oscillating mirror. Specifically, we study the discrete spectrum of created particles in a region of frequencies above the oscillation frequency $ω_0$ of the mirror. We focus our investigation on an oscillation time equal to $2L_0/c$, where $L_0$ is the initial and final length of the cavity, and $c$ is the speed of light. For this oscillation duration, a field mode, after perturbed by the moving mirror, never meets this mirror in motion again, which allows us to exclude this effect of re-interaction on…
Moving mirrors have been known as tractable setups modeling Hawking radiation from black holes. In this paper, motivated by recent developments regarding the black hole information problem, we present extensive studies of moving mirrors in conformal field theories by employing both field theoretic as well as holographic methods. Reviewing first the usual field theoretic formulation of moving mirrors, we construct their gravity dual by resorting to the AdS/BCFT construction. Based on our holographic formulation, we then calculate the time evolution of entanglement entropy in various moving mirr…
We investigate the random motion of a mirror in (1 + 1)-dimensions that is immersed in a thermal bath of massless scalar particles which are interacting with the mirror through a boundary condition. Imposing the Dirichlet or the Neumann boundary conditions on the moving mirror, we evaluate the mean radiation reaction force on the mirror and the correlation function describing the fluctuations in the force about the mean value. From the correlation function thus obtained, we explicitly establish the fluctuation-dissipation theorem governing the moving mirror. Using the fluctuation-dissipation t…
We present new regular solutions of Einstein-charged scalar field theory in a cavity. The system is enclosed inside a reflecting mirror-like boundary, on which the scalar field vanishes. The mirror is placed at the zero of the scalar field closest to the origin, and inside this boundary our solutions are regular. We study the stability of these solitons under linear, spherically symmetric perturbations of the metric, scalar and electromagnetic fields. If the radius of the mirror is sufficiently large, we present numerical evidence for the stability of the solitons. For small mirror radius, som…
We study the effective dynamics of two mirrors, forming an optical cavity, and interacting with the cavity field via radiation pressure. We pursue a perturbative influence functional approach to trace out the degrees-of-freedom of the field, and obtain the second order effective action for the system composed by the mirrors. We find that the interaction between the mirrors is mediated by pairs of field modes, which combine in such a way to give rise to two different interaction channels. We find that the quantum and thermal fluctuations of the cavity field result in coloured, Gaussian stochast…
Accelerating mirrors provide a simple conceptual laboratory for studying particle production and the relation between trajectory and particle, energy, and entropy fluxes. We focus on the relation between energy and entropy, studying some special cases with finite total energy but infinite integrated entropy (though the entropy flux may be finite at any particular moment). We present a new asymptotically static moving mirror trajectory with solvable beta Bogolyubov coefficients, total energy and fully relativistic particle count. The integrated entropy diverges despite finite global radiative p…
We study the Dynamical Casimir Effect (DCE) due to an Abelian gauge field in 2+1 dimensions, in the presence of semitransparent, zero-width mirrors, which may move or deform in a time-dependent way. We obtain general expressions for the probability of motion-induced pair creation, which we render in a more explicit form, for some relevant states of motion.
We investigate the entanglement entropy and the information flow of two-dimensional moving mirrors. Here we point out that various mirror trajectories can help to mimic different candidate resolutions to the information loss paradox following the semi-classical quantum field theory: (i) a suddenly stopping mirror corresponds to the assertion that all information is attached to the last burst, (ii) a slowly stopping mirror corresponds to the assertion that thermal Hawking radiation carries information, and (iii) a long propagating mirror corresponds to the remnant scenario. Based on such analog…
We find the quantum power emitted and distribution in $3+1$-dimensions of relativistic acceleration radiation using a single perfectly reflecting mirror via Lorentz invariance demonstrating close analogies to point charge radiation in classical electrodynamics.
Understanding the entanglement of radiation in QFT has been a long standing challenge, with implications ranging from black hole thermodynamics to quantum information. We demonstrate how the case of the free fermion in $1 + 1$ dimensions reveals the details of the density matrix of the radiation produced by a moving mirror. Using the resolvent method rather than standard CFT techniques we derive the Rényi entropies, modular Hamiltonian and flow of the radiation, and determine when mirrors generate unitary transformations.
The CGHS black hole has a spectrum and temperature that corresponds to an accelerated reflecting boundary condition in flat spacetime. The beta coefficients are identical to a moving mirror model where the acceleration is exponential in laboratory time. The center and the event horizon of the black hole are at the same location modeled by the perfectly reflecting regularity condition that red-shifts the field modes. In addition to computing the energy flux, we find the corresponding parameter associated with the black hole mass and the cosmological constant in the gravitational analog system. …
We analyze the flow of energy and entropy emitted by a class of moving mirror trajectories which provide models for the radiation fields produced by black hole evaporation. The mirror radiation fields provide natural, concrete examples of processes that follow thermal distributions for long periods, accompanied by transients which are brief and carry little net energy, yet they ultimately represent pure quantum states. A burst of negative energy flux is a generic feature of these fields, but it need not be prominent.
We calculate the time evolution of entanglement entropy in two dimensional conformal field theory with a moving mirror. For a setup modeling Hawking radiation, we obtain a linear growth of entanglement entropy and show that this can be interpreted as the production of entangled pairs. For a setup, which mimics black hole formation and evaporation, we find that the evolution follows the ideal Page curve. We perform these computations by constructing the gravity dual of the moving mirror model via holography. We also argue that our holographic setup provides a concrete model to derive the Page c…
Shortcuts to adiabaticity constitute a powerful alternative that speed up time-evolution while mimicking adiabatic dynamics. They are also relevant to clarify fundamental questions such as a precise quantification of the third principle of thermodynamics and quantum speed limits. In this letter we describe, for the first time, how to implement shortcuts to adiabaticity in quantum field theory, for the particular case of a massless scalar field inside a cavity with a moving wall, in 1 + 1 dimensions. The approach is based on the known solution to the problem that exploits the conformal symmetry…
