We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energymomentum tensor and particle current into nondissipative and dissipative parts, and analyze their time evolution in detail. Performing the path-integral formulation of the local Gibbs distribution, we microscopically derive the generating functional for the nondissipative hydrodynamics. We also construct a basis to study dissipative corrections. In particular, we derive the first-order dissipative hydrodynamic equations without a choice of frame such as the Landau-Lifshitz or Eckart frame.

The Lefschetz-thimble approach to path integrals is applied to a one-site model of electrons, i.e., the one-site Hubbard model. Since the one-site Hubbard model shows a non-analytic behavior at the zero temperature and its path integral expression has the sign problem, this toy model is a good testing ground for an idea or a technique to attack the sign problem. Semiclassical analysis using complex saddle points unveils the significance of interference among multiple Lefschetz thimbles to reproduce the non-analytic behavior by using the path integral. If the number of Lefschetz thimbles is insufficient, we found not only large discrepancies from the exact result, but also thermodynamic instabilities. Analyzing such singular behaviors semiclassically, we propose a criterion to identify the necessary number of Lefschetz thimbles. We argue that this interference of multiple saddle points is a key issue to understand the sign problem of the finite-density quantum chromodynamics.

The photovoltaic effect in a Weyl semimetal due to the adiabatic quantum phase is studied. We particularly focus on the case in which an external ac electric field is applied to the semimetal. In this setup, we show that a photocurrent is induced by the ac electric field. By considering a generalized Weyl Hamiltonian with nonlinear terms, it is shown that the photocurrent is induced by circularly, rather than linearly, polarized light. This photovoltaic current can be understood as an emergent electromagnetic induction in the momentum space; the Weyl node is a magnetic monopole in the momentum space, of which the electric field is induced by the circular motion. This result is distinct from conventional photovoltaic effects, and potentially useful for experimentally identifying Weyl semimetals in chiral crystals.Introduction -The non-trivial phase in quantum adiabatic processes -Berry's phase -is one of the fundamental aspects of quantum mechanics. In a quantum system, the presence of an energy gap often prohibits excitation to higher-energy states, and confines electrons within a subspace of the Hilbert space constituted from lower energy states. In dynamical processes, such confinement sometimes gives rise to an additional geometric phase that depends only on the path, not on the details of dynamics.Ever since its first discovery [1], it has been revealed that Berry's phase leads to rich physics distinct from classical systems. Interestingly, the effect of Berry's phase appears not only in mesoscopic systems, but also in macroscopic properties of bulk materials. In solid-state materials, Berry's phase of electrons leads to non-trivial properties of solids, such as fractional pseudorotation quantum numbers in Jahn-Teller systems [2-4] and topological Hall effects [5,6] arising from non-collinear magnetic textures. A similar non-trivial structure of wave functions shows up in the Brillouin zone, and contributes to non-trivial structures in electronic states [7,8], and to transport phenomena [9][10][11].Berry's phase also affects the dynamics of nonequilibrium systems. In periodically driven systems, it is known that the adiabatic phase induces the quantized pumping of charge [12][13][14]. In an insulator, the pumping of charge is related to the time average of the emergent electric field defined by [12]

We discuss the dispersion relations of Nambu-Goldstone (NG) modes associated with spontaneous breaking of internal symmetries at finite temperature and/or density. We show that the dispersion relations of type-A (I) and type-B (II) NG modes are linear and quadratic in momentum, whose imaginary parts are quadratic and quartic, respectively. In both cases, the real parts of the dispersion relations are larger than the imaginary parts when the momentum is small, so that the NG modes can propagate far away. We derive the gap formula for NG modes in the presence of a small explicit breaking term. We also discuss the gapped partners of type-B NG modes, when the expectation values of a charge density and a local operator that break the same symmetry coexist.