All Publications

We clarify the relationship between SU(2)L×SU(2)R restoration in the hadron spectrum, parity doubling, and pion-hadron couplings. © 2006 The American Physical Society.

We recently proposed a new approach to the Casimir effect based on classical ray optics (the "optical approximation"). In this paper we show how to use it to calculate the local observables of the field theory. In particular, we study the energy-momentum tensor and the Casimir pressure. We work three examples in detail: parallel plates, the Casimir pendulum and a sphere opposite a plate. We also show how to calculate thermal corrections, proving that the high temperature 'classical limit' is indeed valid for any smooth geometry. © 2006 Elsevier B.V. All rights reserved.

We construct the most general nonlinear representation of chiral SU(2)L×SU(2)R broken down spontaneously to the isospin SU(2), on a pair of hadrons of same spin and isospin and opposite parity. We show that any such representation is equivalent, through a hadron field transformation, to two irreducible representations on two hadrons of opposite parity with different masses and axial-vector couplings. This implies that chiral symmetry realized in the Nambu-Goldstone mode does not predict the existence of degenerate multiplets of hadrons of opposite parity nor any relations between their couplings or masses. © 2006 The American Physical Society.

We find the exact Casimir force between a plate and a cylinder, a geometry intermediate between parallel plates, where the force is known exactly, and the plate sphere, where it is known at large separations. The force has an unexpectedly weak decay ∼L/[H3ln(H/R)] at large plate-cylinder separations H (L and R are the cylinder length and radius), due to transverse magnetic modes. Path integral quantization with a partial wave expansion additionally gives a qualitative difference for the density of states of electric and magnetic modes, and corrections at finite temperatures. © 2006 The American Physical Society.

Using the statistical description common to random waves and quantum fields we show how the probability of having a nodal line close to a (translationally symmetric) reference curve γ is related to the Casimir energy of an appropriate configuration of conductors. © 2006 IOP Publishing Ltd.

We study the Casimir force acting on a conducting piston with arbitrary cross section. We find the exact solution for a rectangular cross section and the first three terms in the asymptotic expansion for small height to width ratio when the cross section is arbitrary. Though weakened by the presence of the walls, the Casimir force turns out to be always attractive. Claims of repulsive Casimir forces for related configurations, like the cube, are invalidated by cutoff dependence. © 2005 The American Physical Society.

We study the Casimir force between defects (branes) of codimension larger than 1 due to quantum fluctuations of a scalar field living in the bulk. We show that the Casimir force is attractive and that it diverges as the distance between the branes approaches a critical value Lc. Below this critical distance Lc the vacuum state =0 of the theory is unstable, due to the birth of a tachyon, and the field condenses. © 2005 The American Physical Society.

We study the Casimir energy of a massless scalar field that obeys Dirichlet boundary conditions on a hyperboloid facing a plate. We use the optical approximation including the first six reflections and compare the results with the predictions of the proximity force approximation and the semiclassical method. We also consider finite size effects by contrasting the infinite with a finite plate. We find sizable and qualitative differences between the optical method and the more traditional approaches. © 2005 The American Physical Society.

We study the Casimir force on a single surface immersed in an inhomogeneous medium. Specifically we study the vacuum fluctuations of a scalar field with a spatially varying squared mass, m2+λΔ(x-a)+V(x), where V is a smooth potential and Δ(x) is a unit-area function sharply peaked around x ≤ 0. Δ(x-a) represents a semi-penetrable thin plate placed at x ≤ a. In the limits {Δ(x-a)→δ(x-a), λ→∞} the scalar field obeys a Dirichlet boundary condition, φ ≤ 0, at x ≤ a. We formulate the problem in general and solve it in several approximations and specific cases. In all the cases we have studied we find that the Casimir force on the plate points in the direction opposite to the force on the quanta of φ: it pushes the plate toward higher potential, hence our use of the term buoyancy. We investigate Casimir buoyancy for weak, reflectionless, or smooth V(x), and for several explicitly solvable examples. In the semiclassical approximation, which seems to be quite useful and accurate, the Casimir buoyancy is a local function of V(a). We extend our analysis to the analogous problem in n-dimensions with n-1 translational symmetries, where Casimir divergences become more severe. We also extend the analysis to non-zero temperatures.

We present the foundations of a new approach to the Casimir effect based on classical ray optics. We show that a very useful approximation to the Casimir force between arbitrarily shaped smooth conductors can be obtained from knowledge of the paths of light rays that originate at points between these bodies and close on themselves. Although an approximation, the optical method is exact for flat bodies, and is surprisingly accurate and versatile. In this paper we present a self-contained derivation of our approximation, discuss its range of validity and possible improvements, and work out three examples in detail. The results are in excellent agreement with recent precise numerical analysis for the experimentally interesting configuration of a sphere opposite an infinite plane. © 2004 Elsevier B.V. All rights reserved.

We investigate some examples of quantum Zeno dynamics, when a system undergoes very frequent (projective) measurements that ascertain whether it is within a given spatial region. In agreement with previously obtained results, the evolution is found to be unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. By using a new approach to this problem, this result is found to be valid in an arbitrary N-dimensional compact domain. We then propose some preliminary ideas concerning the algebra of observables in the projected region and finally look at the case of a projection onto a lower-dimensional space: in such a situation the Zeno ansatz turns out to be a procedure to impose constraints.

We propose a new approach to the Casimir effect based on classical ray optics. We define and compute the contribution of classical optical paths to the Casimir force between rigid bodies. We reproduce the standard result for parallel plates and agree over a wide range of parameters with a recent numerical treatment of the sphere and plate with Dirichlet boundary conditions. Our approach improves upon the proximity force approximation. It can be generalized easily to other geometries, other boundary conditions, to the computation of Casimir energy densities, and to many other situations. © 2004 The American Physical Society.

The dynamics of a chain of N coupled anharmonic oscillators at intermediate time scales was analyzed analytically and numerically. It was found that at these intermediate time scales the system performs a Brownian motion with a diffusion constant that can be accurately estimated and turns out to be analytically diverging in the coupling constant. As a result, a perturbative approach to this problem appears sensible.

We study the time evolution of a chain of nonlinear oscillators. We focus on the fractal features of the spectral entropy and analyze its characteristic intermediate time scales as a function of the nonlinear coupling. A Brownian motion is recognized with an analytic power-law dependence of its diffusion coefficient on the coupling. © 2003 The American Physical Society.

The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are tackled and solved by requiring the Hermiticity of some operators. The presence of an additional term in the quantum Hamiltonian is discussed. © 2002 Elsevier Science B.V. All rights reserved.

The formation and slow decay of Fermi-Pasta-Ulam (FPU) solitons are proposed to account for dramatic relaxation slowdown. It is emphasized that particular features of such systems enable their production and observation.

The dynamics of a quantum system undergoing frequent measurements was investigated. The quantum Zeno effect yielded ordinary constraints. The system was found to evolve unitarily in a proper subspace of the total Hilbert space by asymptotic analysis. Analysis showed that Zeno dynamics determined the Dirichlet boundary conditions for projections onto spatial regions.

The dynamics of a “kicked” quantum system undergoing repeated measurements of momentum is investigated. A diffusive behavior is obtained even when the dynamics of the classical counterpart is not chaotic. The diffusion coefficient is explicitly computed for a large class of Hamiltonians and compared to the classical case. © 1999 The American Physical Society.