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Physical review research 5(2), L022054 (2023). doi:10.1103/PhysRevResearch.5.L022054, The Casimir effect is a fundamental quantum phenomenon induced by the zero-point energy for a quantum field. It is well known for relativistic fields with a linear dispersion relation, while its existence or absence for nonrelativistic fields with a quadratic dispersion is an unsettled question. Here, we investigate the Casimir effects for various dispersion relations on the lattice. We find that Casimir effects for dispersions proportional to an even power of momentum are absent in a long distance but a remnant of the Casimir effect survives in a short distance. Such a remnant Casimir effect will be experimentally observed in materials with quantum fields on the lattice, such as thin films, narrow nanoribbons, and short nanowires. In terms of this effect, we also give a reinterpretation of the Casimir effect for massive fields., Published by APS, College Park, MD

We investigate the vacuum properties of a massless scalar field theory in constrained spatial geometry, namely, the instantaneous appearance of a thick Dirichlet boundary inside a one-dimensional (1D) Dirichlet cavity and divides it into two parts. Our work presents the calculations for the energy density and particle number density created. The expression of the energy density is found to be dependent on the size nature of the appearing wall, more precisely, it depends on whether the length of the wall is rational or irrational., 9 pages, 4 figures

The Null Energy Condition is considered the most fundamental of the energy conditions, on which several key results, such as the singularity theorems, are based. The Casimir effect is one of the rare equilibrium mechanisms by which it is breached without invoking modified gravity or non-minimal couplings to exotic matter. In this work we propose an independent dynamical mechanism by which it is violated, with the only ingredients being standard (but non-perturbative) QFT and a minimally coupled scalar field in a double-well potential. As for the Casimir effect, we explain why the Averaged Null Energy Condition should not be violated by this mechanism. Nevertheless, the transient behaviour could have profound impacts in Early Universe Cosmology., Comment: 7 pages, 1 figure

1-27 (2021). doi:10.1103/PhysRevResearch.3.023201, The Casimir effect arises from the zero-point energy of particles in momentum space deformed by the existence of two parallel plates. For degrees of freedom on the lattice, its energy-momentum dispersion is determined so as to keep a periodicity within the Brillouin zone, so that its Casimir effect is modified. We study the properties of Casimir effect for lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion based on the Möbius domain-wall fermion formulation, in the 1+1-, 2+1-, and 3+1-dimensional space-time with the periodic or antiperiodic boundary condition. An oscillatory behavior of Casimir energy between odd and even lattice size is induced by the contribution of ultraviolet-momentum (doubler) modes, which realizes in the naive fermion, Wilson fermion in a negative mass, and overlap fermions with a large domain-wall height. Our findings can be experimentally observed in condensed matter systems such as topological insulators and also numerically measured in lattice simulations.

Physics letters / B 809, 135713 (2020). doi:10.1016/j.physletb.2020.135713, We propose a definition of the Casimir energy for free lattice fermions. From this definition, we study the Casimir effects for the massless or massive naive fermion, Wilson fermion, and (Möbius) domain-wall fermion in 1+1 dimensional spacetime with the spatial periodic or antiperiodic boundary condition. For the naive fermion, we find an oscillatory behavior of the Casimir energy, which is caused by the difference between odd and even lattice sizes. For the Wilson fermion, in the small lattice size of N≥3 , the Casimir energy agrees very well with that of the continuum theory, which suggests that we can control the discretization artifacts for the Casimir effect measured in lattice simulations. We also investigate the dependence on the parameters tunable in Möbius domain-wall fermions. Our findings will be observed both in condensed matter systems and in lattice simulations with a small size., Published by North-Holland Publ., Amsterdam

We study, for the first time, the Casimir effect in non-Abelian gauge theory using first-principle numerical simulations. Working in two spatial dimensions at zero temperature we find that closely spaced perfect chromoelectric conductors attract each other with a small anomalous scaling dimension. At large separation between the conductors, the attraction is exponentially suppressed by a new massive quantity, the Casimir mass, which is surprisingly different from the lowest glueball mass. The apparent emergence of the new massive scale may be a result of the backreaction of the vacuum to the presence of the plates as sufficiently close chromoelectric conductors induce, in a space between them, a smooth crossover transition to a color deconfinement phase., 6 pages, 4 figures

International audience; Archimedes is an experiment devoted to measure the weight of zero point energy by weighing acascade of rigid Casimir cavitities costituted by a layered type II superconductor, when the reflec-tivity of the cavities is modulated and thus the energy inside. In this paper the working principleof the experiment is presented and the results of the existing prototype are presented, showingthe torque sensitivity of about 10−11 Nm/sqrtHz in the region of frequency from about 50 mHzup two 150 mHz. Moreover the major upgrades needed to reach the desired final sensitivity arediscussed.

International audience; We study, for the first time, the Casimir effect in non-Abelian gauge theory using first-principles numerical simulations. Working in two spatial dimensions at zero temperature, we find that closely spaced perfect chromoelectric conductors attract each other with a small anomalous scaling dimension. At large separation between the conductors, the attraction is exponentially suppressed by a new massive quantity, the Casimir mass, which is surprisingly different from the lowest glueball mass. The apparent emergence of the new massive scale may be a result of the backreaction of the vacuum to the presence of the plates as sufficiently close chromoelectric conductors induce, in a space between them, a smooth crossover transition to a color deconfinement phase.

In the context of loop quantum gravity (LQG), we study the fate of Thiemann complexifier in homogeneous and isotropic Friedmann-Lemaitre-Roberston-Walker (FLRW) cosmology. The complexifier is the dilatation operator acting on the canonical phase space for gravity and generates the canonical transformations shifting the Barbero-Immirzi parameter. We focus on the closed algebra consisting in the complexifier, the 3d volume and the Hamiltonian constraint, which we call the CVH algebra (for Complexier-Volume-Hamiltonian constraint algebra). In standard cosmology, for gravity coupled to a scalar field, the CVH algebra is identified as a $\mathfrak{su}(1,1)$ Lie algebra, with the Hamiltonian as a null generator, the complexifier as a boost and the $\mathfrak{su}(1,1)$ Casimir given by the matter density. The loop gravity cosmology approach introduces a regularization length scale $\ensuremath{\lambda}$ and regularizes the gravitational Hamiltonian in terms of SU(2) holonomies. We show that this regularization is compatible with the CVH algebra, if we suitably regularize the complexifier and inverse volume factor. The regularized complexifier generates a generalized version of the Barbero's canonical transformation which reduces to the classical one when $\ensuremath{\lambda}\ensuremath{\rightarrow}0$. This structure allows for the exact integration of the actions of the Hamiltonian constraints and the complexifier. This straightforwardly extends to the quantum level: the cosmological evolution is described in terms of SU(1, 1) coherent states and the regularized complexifier generates unitary transformations. The Barbero-Immirzi parameter is to be distinguished from the regularization scale $\ensuremath{\lambda}$, it can be rescaled unitarily and the Immirzi ambiguity ultimately disappears from the physical predictions of the theory. Finally, we show that the complexifier becomes the effective Hamiltonian when deparametrizing the dynamics using the scalar field as a clock, thus underlining the deep relation between cosmological evolution and scale transformations.

International audience; In the context of loop quantum gravity (LQG), we study the fate of Thiemann complexifier in homogeneous and isotropic Friedmann-Lemaitre-Roberston-Walker (FLRW) cosmology. The complexifier is the dilatation operator acting on the canonical phase space for gravity and generates the canonical transformations shifting the Barbero-Immirzi parameter. We focus on the closed algebra consisting in the complexifier, the 3d volume and the Hamiltonian constraint, which we call the CVH algebra (for Complexier-Volume-Hamiltonian constraint algebra). In standard cosmology, for gravity coupled to a scalar field, the CVH algebra is identified as a su(1,1) Lie algebra, with the Hamiltonian as a null generator, the complexifier as a boost and the su(1,1) Casimir given by the matter density. The loop gravity cosmology approach introduces a regularization length scale λ and regularizes the gravitational Hamiltonian in terms of SU(2) holonomies. We show that this regularization is compatible with the CVH algebra, if we suitably regularize the complexifier and inverse volume factor. The regularized complexifier generates a generalized version of the Barbero’s canonical transformation which reduces to the classical one when λ→0. This structure allows for the exact integration of the actions of the Hamiltonian constraints and the complexifier. This straightforwardly extends to the quantum level: the cosmological evolution is described in terms of SU(1, 1) coherent states and the regularized complexifier generates unitary transformations. The Barbero-Immirzi parameter is to be distinguished from the regularization scale λ, it can be rescaled unitarily and the Immirzi ambiguity ultimately disappears from the physical predictions of the theory. Finally, we show that the complexifier becomes the effective Hamiltonian when deparametrizing the dynamics using the scalar field as a clock, thus underlining the deep relation between cosmological evolution and scale transformations.

Universität Hamburg, Diplomarbeit, 2007; 76 pp., (2007). doi:10.3204/DESY-THESIS-2008-001, Published by Deutsches Elektronen-Synchrotron, DESY, Hamburg

Universität Hamburg, Diplomarbeit, 2005; 70 pp., (2005). doi:10.3204/DESY-THESIS-2005-003, Published by Deutsches Elektronen-Synchrotron, DESY, Hamburg