Related papers: Complex singularities around the QCD critical poin…
A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for Q-homology planes with smooth locus of non-general type. We show that if a Q-homology plane contains a non-quotient…
We employ a conformal mapping to explore the thermodynamics of strongly interacting matter at finite values of the baryon chemical potential $\mu$. This method allows us to identify the singularity corresponding to the critical point of a…
In this paper we give a review on the computational methods used to characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the singularity tracking method based on the analysis of the Fourier spectrum.…
The pole structure of the $\Lambda(1405)$ is examined by fitting the couplings of an underlying Hamiltonian effective field theory to cross sections of $K^- p$ scattering in the infinite-volume limit. Finite-volume spectra are then obtained…
Singularity of the potential function makes quantum tunneling problem mathematically underdetermined. To circumvent the difficulties it introduced in physics, a potential singularity cutoff is often used, followed by a reverse limit…
It is shown how the QCD sum rules can be applied for the investigation of the density dependence of the nucleon parameters. These characteristics can be expressed through the expectation values of QCD operators in nuclear matter. In certain…
One of the distinctive feature of the QCD phase diagram is the possible emergence of a critical endpoint. The critical region around the critical point and the path dependency of the critical exponents is investigated within effective…
We revisit the determination of the pseudo-critical line of QCD with four degenerate quarks at non-zero temperature and baryon density by the method of analytic continuation. We determine the pseudo-critical couplings at imaginary chemical…
We discuss how the finiteness of the system created in a heavy-ion collision affects possible signatures of the QCD critical endpoint. We show sizable results for the modifications of the chiral phase diagram at volume scales typically…
Concepts of the complex partition functions and the Fisher zeros provide intrinsic statistical mechanisms for finite temperature and real time dynamical phase transitions. We extend the utility of these complexifications to quantum phase…
We apply the Yang-Lee theory of phase transitions to an urn model of separation of sand. The effective partition function of this nonequilibrium system can be expressed as a polynomial of the size-dependent effective fugacity $z$. Numerical…
We present a general theory of the singularity in the London penetration depth at symmetry-breaking and topological quantum critical points within a superconducting phase. While the critical exponents, and ratios of amplitudes on the two…
We study relativistic massive vector condensation due to a non zero chemical potential associated to some of the global conserved charges of the theory. We show that the phase structure is very rich. More specifically there are three…
A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow up. This is a natural generalization of the surface singularities of types $D_{n}$, $E_{6}$, $E_{7}$ and $E_{8}$. Since this idea was introduced,…
The phase behavior of a cross-linked polymer blend made of two incompatible species, $A$ and $B$, of different chemical nature is analyzed. Besides a homogeneous phase, this system also exhibits two microphases and a phase of total…
We study the Roberge-Weiss phase transition numerically. The phase transition is associated with the discontinuities in the quark-number density at specific values of imaginary quark chemical potential. We parameterize the quark number…
In this thesis work we have employed two microscopic models (ladder-QCD and Nambu-Jona-Lasinio) for describing the properties of the QCD phase diagram at finite temperature and quark densities. In particular, we have studied the mechanism…
We study singularities in the I-V characteristics for sequential tunneling from resonant localized levels (e.g. a quantum dot) into a one dimensional electron system described by a Hubbard model. Boundary conformal field theory together…
We discuss the phase structure and the equation of state for QCD at non-zero temperature and density. Derivatives of $\ln Z$ with respect to quark chemical potential $\mu_q$ up to fourth order are calculated for 2-flavor QCD, enabling…
Physical systems and signals are often characterized by complex functions of frequency in the harmonic-domain. The extension of such functions to the complex frequency plane has been a topic of growing interest as it was shown that specific…