@article{9020,
  abstract     = {We study dynamics and thermodynamics of ion transport in narrow, water-filled channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and the surrounding medium, confining the electric filed to stay mostly within the water-filled channel. Statistical mechanics of such Coulomb systems is dominated by entropic effects which may be accurately accounted for by mapping onto an effective quantum mechanics. In presence of multivalent ions the corresponding quantum mechanics appears to be non-Hermitian. In this review we discuss a framework for semiclassical calculations for the effective non-Hermitian Hamiltonians. Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. We circumvent this issue by applying tools from algebraic topology, such as the Picard-Fuchs equation. We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within narrow, water-filled channels. },
  author       = {Gulden, Tobias and Kamenev, Alex},
  issn         = {1099-4300},
  journal      = {Entropy},
  number       = {1},
  publisher    = {MDPI},
  title        = {{Dynamics of ion channels via non-hermitian quantum mechanics}},
  doi          = {10.3390/e23010125},
  volume       = {23},
  year         = {2021},
}

@article{8198,
  abstract     = {We investigate how the critical driving amplitude at the Floquet many-body localized (MBL) to ergodic phase transition differs between smooth and nonsmooth drives. To this end, we numerically study a disordered spin-1/2 chain which is periodically driven by a sine or square-wave drive over a wide range of driving frequencies. In both cases the critical driving amplitude increases monotonically with the frequency, and at large frequencies it is identical for the two drives. However, at low and intermediate frequencies the critical amplitude of the square-wave drive depends strongly on the frequency, while that of the sinusoidal drive is almost constant over a wide frequency range. By analyzing the density of drive-induced resonances we conclude that this difference is due to resonances induced by the higher harmonics which are present (absent) in the Fourier spectrum of the square-wave (sine) drive. Furthermore, we suggest a numerically efficient method for estimating the frequency dependence of the critical driving amplitudes for different drives which is based on calculating the density of drive-induced resonances. We conclude that delocalization occurs once the density of drive-induced resonances reaches a critical value determined only by the static system.},
  author       = {Diringer, Asaf A. and Gulden, Tobias},
  issn         = {2469-9969},
  journal      = {Physical Review B},
  number       = {21},
  publisher    = {American Physical Society},
  title        = {{Impact of drive harmonics on the stability of Floquet many-body localization}},
  doi          = {10.1103/PhysRevB.103.214204},
  volume       = {103},
  year         = {2021},
}

@article{8199,
  abstract     = {We investigate a mechanism to transiently stabilize topological phenomena in long-lived quasi-steady states of isolated quantum many-body systems driven at low frequencies. We obtain an analytical bound for the lifetime of the quasi-steady states which is exponentially large in the inverse driving frequency. Within this lifetime, the quasi-steady state is characterized by maximum entropy subject to the constraint of fixed number of particles in the system's Floquet-Bloch bands. In such a state, all the non-universal properties of these bands are washed out, hence only the topological properties persist.},
  author       = {Gulden, Tobias and Berg, Erez and Rudner, Mark Spencer and Lindner, Netanel},
  issn         = {2542-4653},
  journal      = {SciPost Physics},
  publisher    = {SciPost Foundation},
  title        = {{Exponentially long lifetime of universal quasi-steady states in topological Floquet pumps}},
  doi          = {10.21468/scipostphys.9.1.015},
  volume       = {9},
  year         = {2020},
}