Probing dynamical criticality near quantum phase transitions

We reveal a prethermal temporal regime upon suddenly quenching to the vicinity of a quantum phase transition in the time evolution of 1D spin chains. The prethermal regime is analytically found to be self-similar, and its duration is governed by the ground-state energy gap. Based on analytical insights and numerical evidence, we show that this critically prethermal regime universally exists independently of the location of the probe site, the presence of weak interactions, or the initial state. Moreover, the resulting prethermal dynamics leads to an out-of-equilibrium scaling function of the order parameter in the vicinity of the transition.Comment: Revised with an analytical theory and improved presentation. Main text: 4 Pages, 2 Figures; Supplementary: 6 Pages, 5 Figure

On the Transport Properties of a Quark-Hadron Coulomb Lattice in the Cores of Neutron Stars

Already more that 40 years ago, it has been suggested that because of the enormous mass densities in the cores of neutron stars, the hadrons in the centers of neutron stars may undergo a phase transition to deconfined quark matter. In this picture, neutron stars could contain cores made of pure (up, down, strange) quark matter which are surrounded by a mixed phase of quarks and hadrons. More than that, because of the competition between the Coulomb and the surface energies associated with the positively charged regions of nuclear matter and negatively charged regions of quark matter, the mixed phase may develop geometrical structures, similarly to what is expected of the sub-nuclear liquid-gas phase transition. In this paper we restrict ourselves to considering the formation of rare phase blobs in the mixed quark-hadron phase. The influence of rare phase blobs on the thermal and transport properties of neutron star matter is investigated. The total specific heat, $c_V$, thermal conductivity, $\kappa$, and electron-blob Bremsstrahlung neutrino emissivities, $\epsilon_{\nu,\text{BR}}$, of quark-hybrid matter are computed and the results are compared with the associated thermal and transport properties of standard neutron star matter. Our results show that the contribution of rare phase blobs to the specific heat is negligibly small. This is different for the neutrino emissivity from electron-blob Bremsstrahlung scattering, which turns out to be of the same order of magnitude as the total contributions from other Bremsstrahlung processes for temperatures below about $10^8$ K.Comment: minor changes, accepted by Phys. Rev.

Limiting Configurations for the SU(1,2) Hitchin Equation

This dissertation studies the SU(1,2) Higgs bundle and a limiting behavior of solutions of the SU(1,2) Hitchin's self-duality equation. On a closed Riemann surface $X$ of genus $g\ge 2$, an SU(1,2) Higgs bundle consists of the following data: a rank two holomorphic vector bundle $F$ and the holomorphic maps $\beta: L\otimes K_X^{-1}\to F$, $\gamma: F\to L\otimes K_X$ where $L=\det F^\ast$. The Hitchin map of the moduli space of SU(1,2) Higgs bundles takes $(F,\beta,\gamma)$ to the quadratic differential $q=\gamma\circ\beta$. For an SU(1,2) Higgs bundle $(F,\beta,\gamma)$, the Hitchin equation is a non-linear PDE of hermitian metric $h$ on $F$. The existence of a unique solution follows from the stability condition. For a stable SU(1,2) Higgs bundle $(F,\beta,\gamma)$, we give an explicit description of the behavior of $h_t$, the unique solution of SU(1,2) Hitchin equation for the family $(F,t\beta,t\gamma)$ in the case where $q$ has simple zeros in the limit $t\to\infty$. In Chapter 1, we review the notion of $G$ Higgs bundles and focus on the case $G=$SU(1,2). The simple zeros of $q=\gamma\circ\beta$ are one of the three types: (1) a zero of $\beta$, (2) a zero of $\gamma$, or (3) neither. We present a stability condition in terms of the number of zeros of each type. We also review notions of the filtered bundle and the wild harmonic bundle. In Chapter 2, we give an explicit description of the fiber of the Hitchin map in terms of a fiber bundle over the Jacobian of $X$ with unirational fibers. The fiber is a GIT quotient of a $\mathbb{C}^\times$-action on $(\mathbb{P}^1)^{4g-4}$. The base parametrizes the choice of a line bundle $L$. The fiber gives parameters for a Hecke modification $\iota: F\to V$ which realizes $F$ as a rank-two locally free subsheaf of $V=L^{-2}K_X\oplus LK_X$. We show that the stable locus is a coarse moduli space of the appropriate moduli functor. In Chapters 3 and 4, we study the Hitchin equation for the family $(F,t\beta,t\gamma)$ as $t\to\infty$. In particular, we show that the limiting configuration $h_\infty$ satisfies the decoupled Hitchin equation and is induced from a harmonic metric $h_L$ on $L$ via the Hecke modification $\iota: F\to V$. The metric $h_L$ is adapted to a filtered line bundle $(L,\underline{\lambda_\infty})$ where the weights $\underline{\lambda_\infty}$ are specified by a rule depending on the types of zeros and their count. We prove the convergence of $h_t$ to $h_\infty$ after appropriate normalizing by gluing local model solutions constructed from wild harmonic bundles on $\mathbb{P}^1$ over disks around the zeros to a solution of the decoupled equation on the complement

Transient SOX9 expression facilitates resistance to androgen-targeted therapy in prostate cancer

Purpose: Patients with metastatic prostate cancer are increasingly presenting with treatment-resistant, androgen receptor-negative/ low (AR /Low) tumors, with or without neuroendocrine characteristics, in processes attributed to tumor cell plasticity. This plasticity has been modeled by Rb1/p53 knockdown/knockout and is accompanied by overexpression of the pluripotency factor, Sox2. Here, we explore the role of the developmental transcription factor Sox9 in the process of prostate cancer therapy response and tumor progression. Experimental Design: Unique prostate cancer cell models that capture AR. / Low stem cell-like intermediates were analyzed for features of plasticity and the functional role of Sox9. Human prostate cancer xenografts and tissue microarrays were evaluated for temporal alterations in Sox9 expression. The role of NF-kB pathway activity in Sox9 overexpression was explored. Results: Prostate cancer stem cell-like intermediates have reduced Rb1 and p53 protein expression and overexpress Sox2 as well as Sox9. Sox9 was required for spheroid growth, and overexpression increased invasiveness and neural features of prostate cancer cells. Sox9 was transiently upregulated in castration-induced progression of prostate cancer xenografts and was specifically overexpressed in neoadjuvant hormone therapy (NHT)-treated patient tumors. High Sox9 expression in NHT-treated patients predicts biochemical recurrence. Finally, we link Sox9 induction to NF-kB dimer activation in prostate cancer cells. Conclusions: Developmentally reprogrammed prostate cancer cell models recapitulate features of clinically advanced prostate tumors, including downregulated Rb1/p53 and overexpression of Sox2 with Sox9. Sox9 is a marker of a transitional state that identifies prostate cancer cells under the stress of therapeutic assault and facilitates progression to therapy resistance. Its expression may index the relative activity of the NF-kB pathway.</p