Psychophysiological modelling and the measurement of fear conditioning

Quantification of fear conditioning is paramount to many clinical and translational studies on aversive learning. Various measures of fear conditioning co-exist, including different observables and different methods of pre-processing. Here, we first argue that low measurement error is a rational desideratum for any measurement technique. We then show that measurement error can be approximated in benchmark experiments by how closely intended fear memory relates to measured fear memory, a quantity that we term retrodictive validity. From this perspective, we discuss different approaches commonly used to quantify fear conditioning. One of these is psychophysiological modelling (PsPM). This builds on a measurement model that describes how a psychological variable, such as fear memory, influences a physiological measure. This model is statistically inverted to estimate the most likely value of the psychological variable, given the measured data. We review existing PsPMs for skin conductance, pupil size, heart period, respiration, and startle eye-blink. We illustrate the benefit of PsPMs in terms of retrodictive validity and translate this into sample size required to achieve a desired level of statistical power. This sample size can differ up to a factor of three between different observables, and between the best, and the current standard, data pre-processing methods

Two-site dynamical mean field theory for the dynamic Hubbard model

At zero temperature, two-site dynamical mean field theory is applied to the Dynamic Hubbard model. The Dynamic Hubbard model describes the orbital relaxation that occurs when two electrons occupy the same site, by using a two-level boson field at each site. At finite boson frequency, the appearance of a Mott gap is found to be enhanced even though it shows a metallic phase with the same bare on-site interaction $U$ in the conventional Hubbard model. The lack of electron-hole symmetry is highlighted through the quasi-particle weight and the single particle density of states at different fillings, which qualitatively differentiates the dynamic Hubbard model from other conventional Hubbard-like models.Comment: 13 pages, 15 figure

Hyperfine splitting in non-relativistic QED: uniqueness of the dressed hydrogen atom ground state

We consider a free hydrogen atom composed of a spin-1/2 nucleus and a spin-1/2 electron in the standard model of non-relativistic QED. We study the Pauli-Fierz Hamiltonian associated with this system at a fixed total momentum. For small enough values of the fine-structure constant, we prove that the ground state is unique. This result reflects the hyperfine structure of the hydrogen atom ground state.Comment: 22 pages, 3 figure

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

WHIZARD 2.2 for Linear Colliders

We review the current status of the WHIZARD event generator. We discuss, in particular, recent improvements and features that are relevant for simulating the physics program at a future Linear Collider.Comment: Talk presented at the International Workshop on Future Linear Colliders (LCWS13), Tokyo, Japan, 11-15 November 201

Exponential localization of hydrogen-like atoms in relativistic quantum electrodynamics

We consider two different models of a hydrogenic atom in a quantized electromagnetic field that treat the electron relativistically. The first one is a no-pair model in the free picture, the second one is given by the semi-relativistic Pauli-Fierz Hamiltonian. We prove that the no-pair operator is semi-bounded below and that its spectral subspaces corresponding to energies below the ionization threshold are exponentially localized. Both results hold true, for arbitrary values of the fine-structure constant, $e^2$, and the ultra-violet cut-off, $\Lambda$, and for all nuclear charges less than the critical charge without radiation field, $Z_c=e^{-2}2/(2/\pi+\pi/2)$. We obtain similar results for the semi-relativistic Pauli-Fierz operator, again for all values of $e^2$ and $\Lambda$ and for nuclear charges less than $e^{-2}2/\pi$.Comment: 37 page

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

A vanishing theorem for operators in Fock space

We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that rotation invariance implies the absence of terms which either create or annihilate only a single particle. We outline an application of this result in an operator theoretic renormalization analysis of Hamilton operators, which occur in non-relativistic qed.Comment: 14 page