Spectral expansion for finite temperature two-point functions and clustering

Recently, the spectral expansion of finite temperature two-point functions in integrable quantum field theories was constructed using a finite volume regularization technique and the application of multidimensional residues. In the present work, the original calculation is revisited. By clarifying some details in the residue evaluations, we find and correct some inaccuracies of the previous result. The final result for contributions involving no more than two particles in the intermediate states is presented. The result is verified by proving a symmetry property which follows from the general structure of the spectral expansion, and also by numerical comparison to the discrete finite volume spectral sum. A further consistency check is performed by showing that the expansion satisfies the cluster property up to the order of the evaluation.Comment: 38 pages, 1 eps figure

Overlap singularity and time evolution in integrable quantum field theory

We study homogeneous quenches in integrable quantum field theory where the initial state contains zero-momentum particles. We demonstrate that the two-particle pair amplitude necessarily has a singularity at the two-particle threshold. Albeit the explicit discussion is carried out for special (integrable) initial states, we argue that the singularity is inevitably present and is a generic feature of homogeneous quenches involving the creation of zero momentum particles. We also identify the singularity in quenches in the Ising model across the quantum critical point, and compute it perturbatively in phase quenches in the quantum sine-Gordon model which are potentially relevant to experiments. We then construct the explicit time dependence of one-point functions using a linked cluster expansion regulated by a finite volume parameter. We find that the secular contribution normally linear in time is modified by a $t\ln t$ term. We additionally encounter a novel type of secular contribution which is shown to be related to parametric resonance. It is an interesting open question to resum the new contributions and to establish their consequences directly observable in experiments or numerical simulations.Comment: 30+45 pages, 7 figure

Rethinking Mackinder’s thoughts: The „Heartland”in the 21st century geopolitics

A klasszikus háború politológiai, politikai filozófiai és geopolitikai koncepciója a 19. századtól a 21. századig átértékelődött vagy átstrukturálódott. Mennyire alkalmazható, megvalósítható és adaptálható Halford John Mackinder „Heartland” elmélete a modern és premodern geopolitikai konfliktusok megoldásában? Hogyan értelmezhetők Mackinder gondolatai a mai modern politikatudományban és geopolitikában? Ezek a kérdések képzik tanulmányom lényegét

Rethinking Mackinder’s thoughts: The „Heartland”in the 21st century geopolitics

A klasszikus háború politológiai, politikai filozófiai és geopolitikai koncepciója a 19. századtól a 21. századig átértékelődött vagy átstrukturálódott. Mennyire alkalmazható, megvalósítható és adaptálható Halford John Mackinder „Heartland” elmélete a modern és premodern geopolitikai konfliktusok megoldásában? Hogyan értelmezhetők Mackinder gondolatai a mai modern politikatudományban és geopolitikában? Ezek a kérdések képzik tanulmányom lényegét

Optimal control of a large dam

A large dam model is an object of study of this paper. The parameters $L^{lower}$ and $L^{upper}$ are its lower and upper levels, $L=L^{upper}-L^{lower}$ is large, and if a current level of water is between these bounds, then the dam is assumed to be in normal state. Passage one or other bound leads to damage. Let $J_1$ $(J_2)$ denote the damage cost of crossing the lower (upper) level. It is assumed that input stream of water is described by a Poisson process, while the output stream is state-dependent (the exact formulation of the problem is given in the paper). Let $L_t$ denote the dam level at time $t$, and let $p_1=\lim_{t\to\infty}\mathbf{P}\{L_t= L^{lower}\}$, $p_2=\lim_{t\to\infty}\mathbf{P}\{L_t> L^{upper}\}$ exist. The long-run average cost $J=p_1J_1+p_2J_2$ is a performance measure. The aim of the paper is to choose the parameter of output stream (exactly specified in the paper) minimizing $J$.Comment: To appear in "Journal of Applied Probability" 44 (2007), No.