The high pressure and high temperature behavior of the energetic molecule 1-fluoro-2,4-dinitrobenzene (DNFB) was studied by Raman spectroscopy in a Diamond Anvil Cell (DAC). The pressure-temperature phase diagram was determined up to 20 GPa and 550 K (thermal decomposition). Between 0 and 15 GPa, two solid-solid phase transitions were suggested from slope changes of the vibrational modes. Above 15 GPa, irreversible chemical transformation was observed.

We study Spectral Measures of Risk from the perspective of portfolio optimization. We derive exact results which extend to general Spectral Measures M_phi the Pflug--Rockafellar--Uryasev methodology for the minimization of alpha--Expected Shortfall. The minimization problem of a spectral measure is shown to be equivalent to the minimization of a suitable function which contains additional parameters, but displays analytical properties (piecewise linearity and convexity in all arguments, absence of sorting subroutines) which allow for efficient minimization procedures. In doing so we also reveal a new picture where the classical risk--reward problem a la Markowitz (minimizing risks with constrained returns or maximizing returns with constrained risks) is shown to coincide to the unconstrained optimization of a single suitable spectral measure. In other words, minimizing a spectral measure turns out to be already an optimization process itself, where risk minimization and returns maximization cannot be disentangled from each other.

Physics and finance are both fundamentally based on the theory of random walks (and their generalizations to higher dimensions) and on the collective behavior of large numbers of correlated variables. The archetype examplifying this situation in finance is the portfolio optimization problem in which one desires to diversify on a set of possibly dependent assets to optimize the return and minimize the risks. The standard mean-variance solution introduced by Markovitz and its subsequent developments is basically a mean-field Gaussian solution. It has severe limitations for practical applications due to the strongly non-Gaussian structure of distributions and the nonlinear dependence between assets. Here, we present in details a general analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto Gaussian variables whose covariance matrix provides a new measure of dependence between the non-normal returns, generalizing the covariance matrix into a nonlinear covariance matrix. This nonlinear covariance matrix is chiseled to the specific fat tail structure of the underlying marginal distributions, thus ensuring stability and good conditioning. The portfolio distribution is then obtained as the solution of a mapping to a so-called φq field theory in particle physics, of which we offer an extensive treatment using Feynman diagrammatic techniques and large deviation theory, that we illustrate in details for multivariate Weibull distributions. The interaction (non-mean field) structure in this field theory is a direct consequence of the non-Gaussian nature of the distribution of asset price returns. We find that minimizing the portfolio variance (i.e. the relatively “small” risks) may often increase the large risks, as measured by higher normalized cumulants. Extensive empirical tests are presented on the foreign exchange market that validate satisfactorily the theory. For “fat tail” distributions, we show that an adequate prediction of the risks of a portfolio relies much more on the correct description of the tail structure rather than on their correlations. For the case of asymmetric return distributions, our theory allows us to generalize the return-risk efficient frontier concept to incorporate the dimensions of large risks embedded in the tail of the asset distributions. We demonstrate that it is often possible to increase the portfolio return while decreasing the large risks as quantified by the fourth and higher-order cumulants. Exact theoretical formulas are validated by empirical tests.

We introduce a faithful representation of the heavy tail multivariate distribution of asset returns, as parsimonious as the Gaussian framework. Using calculation techniques of functional integration and Feynman diagrams borrowed from particle physics, we characterize precisely, through its cumulants of high order, the distribution of wealth variations of a portfolio composed of an arbitrary mixture of assets. This approach makes quantitative and rigorous the well-known fact that minimizing the variance, i.e. the relatively "small" risks, often increases larger risks as measured by higher normalized cumulants and the Value-at-Risk.

We introduce a new family of integrable theories with N bosons and N freely adjustable mass parameters. These theories restrict in particular limits to the “generalized supersymmetric” sine-Gordon models, as well as to the flavor anisotropic chiral Gross Neveu models (studied recently by N. Andrei and collaborators). The scattering theory involves scalar particles that are no bound states, and bears an intriguing resemblance with the results of a sharp cut-off analysis of the Thirring model carried out by Korepin in 1980. Various physical applications are discussed. In particular, we demonstrate that our theories are the appropriate continuum limit of integrable quantum spin chains with mixtures of spins.

In a previous paper, we showed that the problem of tunneling in quantum wires was integrable in the isotropic case g(sigma)=2. In the present work, we continue the exploration of the general phase diagram by looking for other integrable cases. Specifically, we discuss in detail the manifold g(rho) + g(sigma) = 2, where the associated "double sine-6ordon" model is integrable. Transport properties are exactly computed, Surprisingly, the IR fixed points, while having complete reflection of charge and spin currents, do not correspond to two separate leads. Their main characteristic is that they are approached along irrelevant operators of dimension 1 + (1/g(rho)) and 1 + (1/g(sigma)), corresponding to transfer of one electron charge but no spin, or one spin 1/2 but no charge. [S0163-1829(98)05708-7].

We introduce a faithful representation of the heavy tail multivariate distribution of asset returns, as parsimonous as the Gaussian framework. Using calculation techniques of functional integration and Feynman diagrams borrowed from particle physics, we characterize precisely, through its cumulants of high order, the distribution of wealth variations of a portfolio composed of an arbitrary mixture of assets. The portfolio which minimizes the variance, i.e. the relatively small risks, often increases larger risks as measured by higher normalized cumulants and by the Value-at-risk.

We discuss in this paper the behaviour of minimal models of conformal theory perturbed by the operator $\Phi_{13}$ at the boundary. Using the RSOS restriction of the sine-Gordon model, adapted to the boundary problem, a series of boundary flows between different set of conformally invariant boundary conditions are described. Generalizing the "staircase" phenomenon discovered by Al. Zamolodchikov, we find that an analytic continuation of the boundary sinh-Gordon model provides a flow interpolation not only between all minimal models in the bulk, but also between their possible conformal boundary conditions. In the particular case where the bulk sinh-Gordon coupling is turned to zero, we obtain a boundary roaming trajectory in the $c=1$ theory that interpolates between all the possible spin $S$ Kondo models.

We show that the problem of impurity tunneling in a Luttinger liquid of electrons with spin is solvable in the spin isotropic case (g(sigma)=2, g(rho) arbitrary). The resulting integrable model is similar to a two-channel anisotropic Kondo model, but with the impurity spin in a ''cyclic representation'' of the quantum algebra su(2)(q) associated with the anisotropy. Using exact, nonperturbative techniques we study the renormalization-group flow, and compute the de conductance. As expected from the analysis of Kane and Fisher we find that the LR fixed point corresponds to two separate leads. We also prove an exact duality between the UV and IR expansions of the current at vanishing temperature.

The one- and two-particle form factors of the energy operator in the two-dimensional Ising model in a magnetic field at T = Tc are exactly computed within the form factor bootstrap approach. Together with the matrix elements of the magnetisation operator already computed by G. Delfino and G. Mussardo [Nucl. Phys. B 455 (1995) 724], they are used to write down the large distance expansion for the correlators of the two relevant fields of the model.

We approach the study of non-integrable models of two-dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact S-matrix and form factors of the integrable field theories we obtain the first-order corrections to the mass ratios, the vacuum energy density and the S-matrix of the non-integrable theories. As interesting applications of the formalism, we study the scaling region of the Ising model in an external magnetic field at T ∼ Tc and the scaling region around the minimal model M2,7. For these models, a remarkable agreement is observed between the theoretical predictions and the data extracted by a numerical diagonalisation of their Hamiltonian.

It is shown that the scaling operators in the conformal limit of a two-dimensional field theory have massive form factors which obey a simple factorisation property in rapidity space. This has been used to identify such operators within the form factor bootstrap approach. A sum rule which yields the scaling dimension of such operators is also derived.

A non-perturbative method based on the Form Factor bootstrap approach is proposed for the analysis of correlation functions of 2-D massless integrable theories and applied to the massless flow between the Tricritical and the Critical Ising Models.

The $O(n)$ Gross-Neveu model for $n < 2$ presents a massless phase that can be characterized by right-left mover scattering processes. The limit $n \goto 0$ describes the on-shell properties of the random bond Ising model.

The short distance behavior of massive integrable quantum field theories is analyzed in terms of the form factor approach. We show that the on-shell dynamics is compatible with different definitions of the stress-energy tensor Tµν(x) of the theory. In terms of form factors, this is equivalent to having a possible nonzero matrix element F1 of the trace of Tµν on a one-particle state. Each choice of F1 induces a different scaling behavior of the massive theory in the ultraviolet limit.

The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of inhomogeneity to the scattering amplitudes in the bulk. The factorization condition for the new amplitudes gives rise to a set of reflection-transmission equations. The solutions of these equations in the case of a diagonal S-matrix in the bulk are only those with S = ±1. The choice S = −1 corresponds to the Ising model. We compute the exact expressions of the transmission and reflection amplitudes relative to the interaction of the Majorana fermion of the Ising model with the defect. These amplitudes present a weak-strong duality in the coupling constant, the self-dual points being the special values where the defect line acts as a reflecting surface. We also discuss the bosonic case S = 1 which presents instability properties and resonance states. Multi-defect systems which may give rise to a band structure are also considered. The exact expressions of correlation functions is obtained in terms of form factors of the bulk theory and matrix elements of the defect operator.

The factorization condition for the scattering amplitudes of an integrable model with a line of defect gives rise to a set of Reflection-Transmission equations. The solutions of these equations in the case of diagonal $S$-matrix in the bulk are only those with $S =\pm 1$. The choice $S=-1$ corresponds to the Ising model. We compute the transmission and reflection amplitudes relative to the interaction of the Majorana fermion with the defect and we discuss their relevant features.

Using Watson's and the recursive equations satisfied by matrix elements of local operators in two-dimensional integrable models, we compute the form factors of the elementary field φ(x) and the stress-energy tensor Tμν(x) of sinh-Gordon theory. Form factors of operators with higher spin or with different asymptotic behaviour can easily be deduced from them. The value of the correlation functions are saturated by the form factors with lowest number of particle terms. This is illustrated by an application of the form factors of the trace of Tμν(x) to the sum rule of the c-theorem.

We derive the recursive equations for the form factors of the local hermitian operators in the Bullough-Dodd model. At the self-dual point of the theory, the form factors of the fundamental field of the Bullough-Dodd model are equal to those of the fundamental field of the sinh-Gordon model at a specific value of the coupling constant.