Ground States in the Spin Boson Model

We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant lambda. We show that the ground state energy is an analytic function of lambda and that the corresponding ground state can also be chosen to be an analytic function of lambda. No infrared regularization is imposed. Our proof is based on a modified version of the BFS operator theoretic renormalization analysis. Moreover, using a positivity argument we prove that the ground state of the spin-boson model is unique. We show that the expansion coefficients of the ground state and the ground state energy can be calculated using regular analytic perturbation theory

A finite difference solution for the cylindrical expansion of a gas cloud into vacuum

Finite difference method for solution of cylindrical expansion of gas cloud into vacuu

Uniqueness of the ground state in the Feshbach renormalization analysis

In the operator theoretic renormalization analysis introduced by Bach, Froehlich, and Sigal we prove uniqueness of the ground state.Comment: 10 page

Field evolution of the magnetic structures in Er2_2Ti2_2O7_7 through the critical point

We have measured neutron diffraction patterns in a single crystal sample of the pyrochlore compound Er$_2$Ti$_2$O$_7$ in the antiferromagnetic phase (T=0.3\,K), as a function of the magnetic field, up to 6\,T, applied along the [110] direction. We determine all the characteristics of the magnetic structure throughout the quantum critical point at $H_c$=2\,T. As a main result, all Er moments align along the field at $H_c$ and their values reach a minimum. Using a four-sublattice self-consistent calculation, we show that the evolution of the magnetic structure and the value of the critical field are rather well reproduced using the same anisotropic exchange tensor as that accounting for the local paramagnetic susceptibility. In contrast, an isotropic exchange tensor does not match the moment variations through the critical point. The model also accounts semi-quantitatively for other experimental data previously measured, such as the field dependence of the heat capacity, energy of the dispersionless inelastic modes and transition temperature.Comment: 7 pages; 8 figure

ROLE OF H-2 LYMPHOCYTE-DEFINED AND SEROLOGICALLY-DEFINED COMPONENTS IN THE GENERATION OF CYTOTOXIC LYMPHOCYTES

The cell-mediated lympholytic capability of mouse spleen cells stimulated in mixed lymphocyte culture is determined by lymphocyte-defined (LD) and serologically-defined (SD) antigenic differences present during sensitization. Cells which are activated by LD differences alone are markedly less effective in causing lysis of target cells. This lack of cytotoxicity is shown to be, at least in part, due to the inability of LD differences to allow the efficient generation of cytotoxic lymphocytes. SD antigens not only serve as good targets for CML but are also shown to be important for the generation of cytotoxic lymphocytes during the mixed lymphocyte culture

GENETIC CONTROL OF CELL-MEDIATED LYMPHOLYSIS IN MOUSE

H-2 congenic mouse strains were tested in vitro to investigate the genetic control of cell-mediated lympholysis (CML). Combinations were selected such that differences in various segments of H-2 could be examined for their ability to stimulate production of effector cells and to serve as targets for lysis. Particular emphasis was directed towards understanding the roles of LD and SD. SD-region differences are important in the sensitization of effector cells and they also function as strong targets for lysis, or as markers for the CML targets. LD differences are also important for sensitization of cytotoxic effector cells, but they serve only as very weak targets for lysis. Collaboration occurs between LD and SD in generation of CML. The nature of this interaction can be of two types: together LD and SD can produce CML which neither difference alone can stimulate; LD can enhance a CML response stimulated by SD-region differences alone

Kramers degeneracy theorem in nonrelativistic QED

Degeneracy of the eigenvalues of the Pauli-Fierz Hamiltonian with spin 1/2 is proven by the Kramers degeneracy theorem. The Pauli-Fierz Hamiltonian at fixed total momentum is also investigated.Comment: LaTex, 11 page

Ground State and Resonances in the Standard Model of Non-relativistic QED

We prove existence of a ground state and resonances in the standard model of the non-relativistic quantum electro-dynamics (QED). To this end we introduce a new canonical transformation of QED Hamiltonians and use the spectral renormalization group technique with a new choice of Banach spaces.Comment: 50 pages change

Optical conductivity for a dimer in the Dynamic Hubbard model

The Dynamic Hubbard Model represents the physics of a multi-band Hubbard model by using a pseudo-spin degree of freedom to dynamically modify the on-site Coulomb interaction. Here we use a dimer system to obtain analytical results for this model. The spectral function and the optical conductivity are calculated analytically for any number of electrons, and the distribution of optical spectral weight is analyzed in great detail. The impact of polaron-like effects due to overlaps between pseudo-spin states on the optical spectral weight distribution is derived analytically. Our conclusions support results obtained previously with different models and techniques: holes are less mobile than electrons.Comment: 11 pages, 4 figure

Improved Lieb-Oxford exchange-correlation inequality with gradient correction

We prove a Lieb-Oxford-type inequality on the indirect part of the Coulomb energy of a general many-particle quantum state, with a lower constant than the original statement but involving an additional gradient correction. The result is similar to a recent inequality of Benguria, Bley and Loss, except that the correction term is purely local, which is more usual in density functional theory. In an appendix, we discuss the connection between the indirect energy and the classical Jellium energy for constant densities. We show that they differ by an explicit shift due to the long range of the Coulomb potential.Comment: Final version to appear in Physical Review A. Compared to the very first version, this one contains an appendix discussing the link with the Jellium proble