相关论文: The boundary F-theorem for free fields
We consider the case of a free real massive bulk scalar in D=4 dimensions, and embed two parallel plates as interfaces on which we impose non-linear boundary conditions, either Dirichlet- or Neumann-like, parameterized by a new coupling…
The variation of the energy for a gravitational system is directly defined from the Hamiltonian field equations of General Relativity. When the variation of the energy is written in a covariant form it splits into two (covariant)…
In this work, we propose a method for calculating the free energy of anisotropic classical spin systems. We use a Hubbard-Stratonovich transformation to express the partition function of a generic bilinear super-exchange Hamiltonian in…
Today's textbooks of electromagnetism give the particular solution to Maxwell's equations involving the integral over the charge and current sources at retarded times. However, the texts fail to emphasize the role played by the choice of…
It is investigated how the shielding of a moving point charge in a one-component fully degenerate fermion plasma affects the bound states near the charge at velocities smaller than the Fermi one. The shielding is accounted for by using the…
The Casimir force between two perfectly reflecting parallel plates is considered. In a recent paper we presented generalised physical boundary conditions describing perfectly reflecting parallel plates. These boundary conditions are…
For arbitrary Ising-like models of any dimension and Hamiltonians with a finite support with all possible multispin interactions and boundary conditions with a shift, the exact value of the free energy in the thermodynamic limit is obtained…
The $N$-particle free fermion state for quantum particles in the plane subject to a perpendicular magnetic field, and with doubly periodic boundary conditions, is written in a product form. The absolute value of this is used to formulate an…
The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the general selfadjoint boundary condition at the origin. When the matrix potential is integrable, the high-energy asymptotics are…
We consider the spin-S ferromagnetic Heisenberg model in three dimensions, in the absence of an external field. Spin wave theory suggests that in a suitable temperature regime the system behaves effectively as a system of non-interacting…
We first study a free particle on an $(n-1)$-sphere in an extended phase space, where the originally second-class Hamiltonian and constraints are now in strong involution. This allows for a Schr\"odinger representation and a Hamilton-Jacobi…
We investigate general semilinear (obstacle-like) problems of the form $\Delta u = f(u)$, where $f(u)$ has a singularity/jump at $\{u=0\}$ giving rise to a free boundary. Unlike many works on such equations where $f$ is approximately…
We consider the possibility of energy being exchanged between the scalar and matter fields in scalar-tensor theories of gravity. Such an exchange provides a new mechanism which can drive variations in the gravitational 'constant' G. We find…
When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…
We obtain the spectral and resolvent estimates for semiclassical pseudodifferential operators with symbol of Gevrey-$s$ regularity, near the boundary of the range of the principal symbol. We prove that the boundary spectrum free region is…
We study the ground-state energy of one-dimensional, non-interacting fermions subject to an external potential in the thermodynamic limit. To this end, we fix some (Fermi) energy $\nu>0$, confine fermions with total energy below $\nu$…
We compute the high-dimensional limit of the free energy associated with a multi-layer generalized linear model. Under certain technical assumptions, we identify the limit in terms of a variational formula. The approach is to first show…
We introduce a general, simple and effective method of evaluating the zero point energy of a quantum field under the influence of arbitrary boundary conditions imposed on the field on flat surfaces perpendicular to a chosen spatial…
We consider equations of the form $\Delta u +\lambda^2 V(x)e^{\,u}=\rho$ in various two dimensional settings. We assume that $V>0$ is a given function, $\lambda>0$ is a small parameter and $\rho=\mathcal O(1)$ or $\rho\to +\infty$ as…
We construct the boundary phase space in $D$-dimensional Einstein gravity with a generic given co-dimension one null surface ${\cal N}$ as the boundary. The associated boundary symmetry algebra is a semi-direct sum of diffeomorphisms of…