We formulate the RNA folding problem as an N ×N matrix field theory. This matrix formalism allows us to give a systematic classification of the terms in the partition function according to their topological character. The theory is set up in such a way that the limit N →∞ yields the so-called secondary structure (Hartree theory). Tertiary structure and pseudo-knots are obtained by calculating t...

We study the spin-ordering and the magnon collective modes of the twodimensional Wigner crystal state at strong magnetic fields. Our work is based on the Hartree-Fock approximation for the ground state and the timedependent Hartree-Fock approximation for the collective modes. We find that the ground state is ferromagnetic, i.e., that all spins are aligned at T = 0 even when the electronic g-fac...

The accuracy of two widely used scalar relativistic Hartree-Fock pseudopotentials, the Trail-Needs-Dirac-Fock (TNDF) and the Burkatzki-Filippi-Dolg (BFD) pseudopotentials, is assessed. The performance of the pseudopotentials is tested for a chemically representative set of 34 first-row molecules. All comparisons are made at the Hartree-Fock level of theory, and both sets of pseudopotentials giv...

For homogeneous initial conditions, Hartree (gaussian) dynamical approximations are known to have problems with thermalization, because of insufficient scattering. We attempt to improve on this by writing an arbitrary density matrix as a superposition of gaussian pure states and applying the Hartree approximation to each member of such an ensemble. Particles can then scatter via their back-reac...

The Hartree-Fock-Bogoliubov (HFB) equations in coordinate representation are solved exactly, i.e., with correct asymptotic boundary conditions for the continuous spectrum. The calculations are performed with effective Skyrme interactions. The exact HFB solutions are compared with HFB calculations based on box boundary conditions and with resonant continuum Hartree-Fock-BCS (HF-BCS) results. The...

We study the Hartree-Fock-Bogoliubov mean-field theory as applied to a two-dimensional finite trapped Bose gas at low temperatures and find that, in the Hartree-Fock approximation, the system can be described either with or without the presence of a condensate; this is true in the thermodynamic limit as well. We are unable to find condensate solutions when we consider a scheme that predicts the...

Modern problems of physical chemistry lead to computations of many-particle potentials and related integral transforms, involving quantities described by higher-order tensors. Conventional numerical treatment of these problems suffers from the so-called “curse of dimensionality”. Recently developed Tucker and canonical tensor approximation techniques provide structured data-sparse representatio...

We investigate spontaneous interlayer phase coherence and the occurrence of the quantum Hall effect in triple-layer electron systems. Our work is based on a simple tight-binding model that greatly facilitates calculations and whose accuracy is verified by comparison with recent experiments. By calculating the ground state in an unrestricted Hartree-Fock approximation and the collective-mode spe...

A multiresolution solver is presented for all-electron Hartree-Fock and Kohn-Sham equations for general polyatomic molecules. The distinguishing features of our numerical solver are that the basis error is eliminated within a user-specified precision, the computational cost of applying operators scales linearly with the number of parameters in a correct physical sense, and the equations are sol...

We consider a quantum system constituted by N identical particles interacting by means of a mean-field Hamiltonian. It is well known that, in the limit N → ∞, the one-particle state obeys to the Hartree equation. Moreover, propagation of chaos holds. In this paper, we take care of the ~ dependence by considering the semiclassical expansion of the N -particle system. We prove that each term of t...