Search results for "Mathematica"
showing 10 items of 7971 documents
Misinterpretation risks of global stochastic optimisation of kinetic models revealed by multiple optimisation runs
2016
Abstract One of use cases for metabolic network optimisation of biotechnologically applied microorganisms is the in silico design of new strains with an improved distribution of metabolic fluxes. Global stochastic optimisation methods (genetic algorithms, evolutionary programing, particle swarm and others) can optimise complicated nonlinear kinetic models and are friendly for unexperienced user: they can return optimisation results with default method settings (population size, number of generations and others) and without adaptation of the model. Drawbacks of these methods (stochastic behaviour, undefined duration of optimisation, possible stagnation and no guaranty of reaching optima) cau…
A many-body approach to transport in quantum systems : From the transient regime to the stationary state
2022
We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green's function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques w…
A quantum statistical approach to simplified stock markets
2009
We use standard perturbation techniques originally formulated in quantum (statistical) mechanics in the analysis of a toy model of a stock market which is given in terms of bosonic operators. In particular we discuss the probability of transition from a given value of the {\em portfolio} of a certain trader to a different one. This computation can also be carried out using some kind of {\em Feynman graphs} adapted to the present context.
Portfolio optimisation with strictly positive transaction costs and impulse control
1998
One crucial assumption in modern portfolio theory of continuous-time models is the no transaction cost assumption. This assumption normally leads to trading strategies with infinite variation. However, following such a strategy in the presence of transaction costs will lead to immediate ruin. We present an impulse control approach where the investor can change his portfolio only finitely often in finite time intervals. Further, we consider transaction costs including a fixed and a proportional cost component. For the solution of the resulting control problems we present a formal optimal stopping approach and an approach using quasi-variational inequalities. As an application we derive a non…
Simulation of BSDEs with jumps by Wiener Chaos Expansion
2016
International audience; We present an algorithm to solve BSDEs with jumps based on Wiener Chaos Expansion and Picard's iterations. This paper extends the results given in Briand-Labart (2014) to the case of BSDEs with jumps. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. Concerning the error, we derive explicit bounds with respect to the number of chaos, the discretization time step and the number of Monte Carlo simulations. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.
Domains of time-dependent density-potential mappings
2011
The key element in time-dependent density functional theory is the one-to-one correspondence between the one-particle density and the external potential. In most approaches this mapping is transformed into a certain type of Sturm-Liouville problem. Here we give conditions for existence and uniqueness of solutions and construct the weighted Sobolev space they lie in. As a result the class of v-representable densities is considerably widened with respect to previous work.
Newton algorithm for Hamiltonian characterization in quantum control
2014
We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank-Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown paramete…
Large-distance asymptotic behaviour of multi-point correlation functions in massless quantum models
2014
We provide a microscopic model setting that allows us to readily access to the large-distance asymptotic behaviour of multi-point correlation functions in massless, one-dimensional, quantum models. The method of analysis we propose is based on the form factor expansion of the correlation functions and does not build on any field theory reasonings. It constitutes an extension of the restricted sum techniques leading to the large-distance asymptotic behaviour of two-point correlation functions obtained previously.
Integrable Hamiltonian systems with swallowtails
2010
International audience; We consider two-degree-of-freedom integrable Hamiltonian systems with bifurcation diagrams containing swallowtail structures. The global properties of the action coordinates in such systems together with the parallel transport of the period lattice and corresponding quantum cells in the joint spectrum are described in detail. The relation to the concept of bidromy which was introduced in Sadovski´ı and Zhilinski´ı (2007 Ann. Phys. 322 164–200) is discussed.
Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials
2019
We investigate signatures of convergence for a sequence of diffusion processes on a line, in conservative force fields stemming from superharmonic potentials $U(x)\sim x^m$, $m=2n \geq 2$. This is paralleled by a transformation of each $m$-th diffusion generator $L = D\Delta + b(x)\nabla $, and likewise the related Fokker-Planck operator $L^*= D\Delta - \nabla [b(x)\, \cdot]$, into the affiliated Schr\"{o}dinger one $\hat{H}= - D\Delta + {\cal{V}}(x)$. Upon a proper adjustment of operator domains, the dynamics is set by semigroups $\exp(tL)$, $\exp(tL_*)$ and $\exp(-t\hat{H})$, with $t \geq 0$. The Feynman-Kac integral kernel of $\exp(-t\hat{H})$ is the major building block of the relaxatio…