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Register a new userCharged particles interaction in both a finite volume and a uniform magnetic field II: topological and analytic properties of a magnetic system
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In present work, we discuss some topological features of charged particles interacting a uniform magnetic field in a finite volume. The edge state solutions are presented, as a signature of non-trivial topological systems, the energy spectrum of edge states show up in the gap between allowed energy bands. By treating total momentum of two-body system as a continuous distributed parameter in complex plane, the analytic properties of solutions of finite volume system in a magnetic field is also discussed.
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A formalism for describing charged particles interaction in both a finite volume and a uniform magnetic field is presented. In the case of short-range interaction between charged particles, we show that the factorization between short-range physics and finite volume long-range correlation effect is possible, a Luscher formula-like quantization condition is thus obtained.
The volume-dependence of a shallow three-particle bound state in the cubic box with a size $L$ is studied. It is shown that, in the unitary limit, the energy-level shift from the infinite-volume position is given by $Delta E=c (kappa^2/m),(kappa L)^{-3/2}|A|^2 exp(-2kappa L/sqrt{3})$, where $kappa$ is the bound-state momentum and $|A|^2$ denotes the three-body analog of the asymptotic normalization constant, which encodes the information about the short-range interactions in the three-body system.
We study the topological susceptibility and the fourth cumulant of the QCD vacuum in the presence of a uniform, background magnetic field in two-and-flavor QCD finding model-independent sum rules relating the shift in the topological susceptibility due to the background magnetic field to the shift in the quark condensates, and the shift in the fourth cumulant to the shifts in the quark condensates and susceptibilities.
In this talk I present the formalism we have used to analyze Lattice data on two meson systems by means of effective field theories. In particular I present the results obtained from a reanalysis of the lattice data on the $KD^{(*)}$ systems, where the states $D^*_{s0}(2317)$ and $D^*_{s1}(2460)$ are found as bound states of $KD$ and $KD^*$, respectively. We confirm the presence of such states in the lattice data and determine the contribution of the $KD$ channel in the wave function of $D^*_{s0}(2317)$ and that of $KD^*$ in the wave function of $D^*_{s1}(2460)$. Our findings indicate a large meson-meson component in the two cases.
We solve the Schrodinger equation for a charged particle in the non-uniform magnetic field by using the Nikiforov-Uvarov method. We find the energy spectrum and the wave function, and present an explicit relation for the partition function. We give analytical expressions for the thermodynamic properties such as mean energy and magnetic susceptibility, and analyze the entropy, free energy and specific heat of this system numerically. It is concluded that the specific heat and magnetic susceptibility increase with external magnetic field strength and different values of the non-uniformity parameter, $alpha$, in the low temperature region, while the mentioned quantities are decreased in high temperature regions due to increasing the occupied levels at these regions. The non-uniformity parameter has the same effect with a constant value of the magnetic field on the behavior of thermodynamic properties. On the other hand, the results show that transition from positive to negative magnetic susceptibility depends on the values of non-uniformity parameter in the constant external magnetic field.
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