Computation of Structure Functions From a Lattice Hamiltonian

We compute structure functions in the Hamiltonian formalism on a momentum lattice using a physically motivated regularisation that links the maximal parton number to the lattice size. We show for the $\phi ^4 _{3+1}$ theory that our method allows to describe continuum physics. The critical line and the renormalised mass spectrum close to the critical line are computed and scaling behaviour is observed in good agreement with L{\"u}scher and Weisz' lattice results. We then compute distribution functions and find a $Q^2$ behaviour and the typical peak at $x_B\rightarrow 0$ like in $QCD$.Comment: 4 pages, three figures. Submitted to Phys.Rev.Let

Monte Carlo Hamiltonian: Inverse Potential

The Monte Carlo Hamiltonian method developed recently allows to investigate ground state and low-lying excited states of a quantum system, using Monte Carlo algorithm with importance sampling. However, conventional MC algorithm has some difficulties when applying to inverse potentials. We propose to use effective potential and extrapolation method to solve the problem. We present examples from the hydrogen system.Comment: To appear in Communications in Theoretical Physic

Modeling thalamocortical cell: impact of Ca2+ channel distribution and cell geometry on firing pattern

The influence of calcium channel distribution and geometry of the thalamocortical cell upon its tonic firing and the low threshold spike (LTS) generation was studied in a 3-compartment model, which represents soma, proximal and distal dendrites as well as in multi-compartment model using the morphology of a real reconstructed neuron. Using an uniform distribution of Ca2+ channels, we determined the minimal number of low threshold voltage-activated calcium channels and their permeability required for the onset of LTS in response to a hyperpolarizing current pulse. In the 3-compartment model, we found that the channel distribution influences the firing pattern only in the range of 3% below the threshold value of total T-channel density. In the multi-compartmental model, the LTS could be generated by only 64% of unequally distributed T-channels compared to the minimal number of equally distributed T-channels. For a given channel density and injected current, the tonic firing frequency was found to be inversely proportional to the size of the cell. However, when the Ca2+ channel density was elevated in soma or proximal dendrites, then the amplitude of LTS response and burst spike frequencies were determined by the ratio of total to threshold number of T-channels in the cell for a specific geometry

Monte Carlo Hamiltonian: the Linear Potentials

We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method, in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. We consider two quantum mechanical models: a symmetric one $V(x) = |x|/2$; and an asymmetric one $V(x)=\infty$, for $x < 0$ and $V(x)=x$, for $x \ge 0$. The results for the spectrum, wave functions and thermodynamical observables are in agreement with the analytical or Runge-Kutta calculations.Comment: Latex file, 8 figure