Nonlinear dynamical Casimir effect at weak nonstationarity

Abstract

We show that even small nonlinearities significantly affect particle production in the dynamical Casimir effect at large evolution times. To that end, we derive the effective Hamiltonian and resum leading loop corrections to the particle flux in a massless scalar field theory with time-dependent Dirichlet boundary conditions and quartic self-interaction. To perform the resummation, we assume small deviations from the equilibrium and employ a kind of rotating wave approximation. Besides that, we consider a quantum circuit analog of the dynamical Casimir effect, which is also essentially nonlinear. In both cases, loop contributions to the number of created particles are comparable to the tree-level values.

arXiv comment15 pages + appendices, 3 figures. v4: discussion extended

References in corpus (56)

• Circuit Quantum Electrodynamics
• Observation of the Dynamical Casimir Effect in a Superconducting Circuit
• Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits
• Introduction to Nonequilibrium Quantum Field Theory
• Dynamical Casimir effect in a Josephson metamaterial
• Black-box superconducting circuit quantization
• Generalized rotating-wave approximation for arbitrarily large coupling
• Motion Induced Radiation from a Vibrating Cavity
• Current status of the Dynamical Casimir Effect
• The dynamical Casimir effect in superconducting microwave circuits
• Josephson junction-embedded transmission-line resonators: from Kerr medium to in-line transmon
• Infrared Sensitivity of Unstable Vacua
• Lecture notes on interacting quantum fields in de Sitter space
• Infrared dynamics in de Sitter space from Schwinger-Dyson equations
• Trembling cavities in the canonical approach
• Networks of nonlinear superconducting transmission line resonators
• Creation of photons in an oscillating cavity with two moving mirrors
• Infrared instability of the de Sitter space
• Hawking radiation and secularly growing loop corrections
• Scalar field correlator in de Sitter space at next-to-leading order in a 1/N expansion
• Characters of different secular effects in various patches of de Sitter space
• Time Dependence of Particle Creation from Accelerating Mirrors
• Many-body theory of non-equilibrium systems
• Resonance Photon Generation in a Vibrating Cavity
• Infrared dynamics of massive scalars from the complementary series in de Sitter space
• Renormalization Group Approach to the Dynamical Casimir Effect
• Kerr non-linearity in a superconducting Josephson metamaterial
• Nonequilibrium Quantum Fields: From Cold Atoms to Cosmology
• Secularly growing loop corrections in strong electric fields
• Quantum analysis of a nonlinear microwave cavity-embedded dc SQUID displacement detector
• Notes on moving mirrors
• Long distance behavior of $O(N)$-model correlators in de Sitter space and the resummation of secular terms
• Physical momentum representation of scalar field correlators in de Sitter space
• Uniformly Accelerated Mirrors. Part 2: Quantum Correlations
• Curved space equilibration vs. flat space thermalization (a short review)
• CP(N-1) model on finite interval in the large N limit
• Dynamical Casimir effect in a Kerr Cavity
• Dynamical Casimir effect and surprises with loop corrections to it
• Self-Consistent Large-$N$ Analytical Solutions of Inhomogneous Condensates in Quantum $\mathbb{C}{P}^{N-1}$ Model
• Casimir Force for the $\mathbb{C}{P}^{N-1}$ Model
• Quantum fields in the future Rindler wedge
• CP(N) sigma model on a finite interval revisited
• Particle creation in nonstationary large N quantum mechanics
• Comments on QED with background electric fields
• A quantum heating as an alternative of reheating
• Dynamical Casimir effect in nonlinear vibrating cavities
• Comments on the adiabatic theorem
• On quantization in background scalar fields
• Secularly growing loop corrections in scalar wave background
• Secularly growing loop corrections to the dynamical Casimir effect
• A few more comments on secularly growing loop corrections in strong electric fields
• Large-N CP(N-1) sigma model on a finite interval: physical boundary effects
• Out of equilibrium two-dimensional Yukawa theory in a strong scalar wave background
• The Casimir effect for nonlinear sigma models and the Mermin-Wagner-Hohenberg-Coleman theorem
• On instability of ground states in 2D CP(N-1) and O(N) models at large N
• Inhomogeneous states in two dimensional linear sigma model at large N

Cited by in corpus (7)

• Enhancement of particle creation in nonlinear resonant cavities
• Loop corrections to a cosmological particle creation
• Dynamical Casimir effect via modulated Kerr or higher nonlinearities
• Thermodynamic entropy production in the dynamical Casimir effect
• Dynamical Casimir effect with screened scalar fields
• Loop corrections to the current of created pairs in the lengthy electric pulse
• Particle Creation and Entanglement in Dispersive Model with Step Velocity Profile