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1. Evidence of a liquid–liquid phase transition in H$$_2$$O and D$$_2$$O from path-integral molecular dynamics simulations

   https://doi.org/10.1038/s41598-022-09525-x  

   Eltareb, Ali ; Lopez, Gustavo E. ; Giovambattista, Nicolas ( April 2022 , Scientific Reports)

   We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H$$_2$$${}_2$O and D$$_2$$${}_2$O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density$$\rho (T)$$$\rho \left(T\right)$, isothermal compressibility$$\kappa _T(T)$$${\kappa }_T\left(T\right)$, and self-diffusion coefficientsD(T) of H$$_2$$${}_2$O and D$$_2$$${}_2$O are in excellent agreement with available experimental data; the isobaric heat capacity$$C_P(T)$$$C_P\left(T\right)$obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H$$_2$$${}_2$O and D$$_2$$${}_2$O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H$$_2$$${}_2$O and D$$_2$$${}_2$O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS). Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H$$_2$$${}_2$O, from PIMD simulations, is located at$$P_c = 167 \pm 9$$$P_c=167\pm 9$ MPa,$$T_c = 159 \pm 6$$$T_c=159\pm 6$ K, and$$\rho _c = 1.02 \pm 0.01$$${\rho }_c=1.02\pm 0.01$ g/cm$$^3$$${}^3$. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D$$_2$$${}_2$O is estimated to be$$P_c = 176 \pm 4$$$P_c=176\pm 4$ MPa,$$T_c = 177 \pm 2$$$T_c=177\pm 2$ K, and$$\rho _c = 1.13 \pm 0.01$$${\rho }_c=1.13\pm 0.01$ g/cm$$^3$$${}^3$. Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effectsmore »(i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of q-TIP4P/F water,$$P_c = 203 \pm 4$$$P_c=203\pm 4$ MPa,$$T_c = 175 \pm 2$$$T_c=175\pm 2$ K, and$$\rho _c = 1.03 \pm 0.01$$${\rho }_c=1.03\pm 0.01$ g/cm$$^3$$${}^3$). Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. The reported values of$$T_c$$$T_c$for D$$_2$$${}_2$O and, particularly, H$$_2$$${}_2$O suggest that improved water models are needed for the study of supercooled water.

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2. Weyl Fermions and broken symmetry phases of laterally confined ³ He films

   https://doi.org/10.1088/1361-648X/acf42b  

   Wu, Hao ; Sauls, J. A. ( September 2023 , Journal of Physics: Condensed Matter)

   Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D)³He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum,$L_z=(N/2)\hslash$, for$N/2$Cooper pairs. The power law suppression of the angular momentum,$L_z(T)\simeq (N/2)\hslash [1-\frac{2}{3}(\pi T/\mathrm{\Delta }{)}^2]$for$0⩽T\ll T_c$, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid³He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry at$D_{c2}\sim 16{\xi }_0$. The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement length$D\to D_{c_2}$. The PDW phase breaks time-reversal symmetry, translation invariance, butmore »is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral ‘polar phase’ at$D_{c1}\sim 9{\xi }_0$, in which a single p-wave orbital state of Cooper pairs is aligned along the channel.

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3. Non-simple conformal loop ensembles on Liouville quantum gravity and the law of CLE percolation interfaces

   https://doi.org/10.1007/s00440-021-01070-4  

   Miller, Jason ; Sheffield, Scott ; Werner, Wendelin ( June 2021 , Probability Theory and Related Fields)

   We study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loop-ensemble$$\hbox {CLE}_{\kappa '}$$${\text{CLE}}_{{\kappa }^{\prime }}$for$$\kappa '$$${\kappa }^{\prime }$in (4, 8) that is drawn on an independent$$\gamma $$$\gamma$-LQG surface for$$\gamma ^2=16/\kappa '$$${\gamma }^2=16/{\kappa }^{\prime }$. The results are similar in flavor to the ones from our companion paper dealing with$$\hbox {CLE}_{\kappa }$$${\text{CLE}}_{\kappa }$for$$\kappa $$$\kappa$in (8/3, 4), where the loops of the CLE are disjoint and simple. In particular, we encode the combined structure of the LQG surface and the$$\hbox {CLE}_{\kappa '}$$${\text{CLE}}_{{\kappa }^{\prime }}$in terms of stable growth-fragmentation trees or their variants, which also appear in the asymptotic study of peeling processes on decorated planar maps. This has consequences for questions that do a priori not involve LQG surfaces: In our paper entitled “CLE Percolations” described the law of interfaces obtained when coloring the loops of a$$\hbox {CLE}_{\kappa '}$$${\text{CLE}}_{{\kappa }^{\prime }}$independently into two colors with respective probabilitiespand$$1-p$$$1-p$. This description was complete up to one missing parameter$$\rho $$$\rho$. The results of the present paper about CLE on LQG allow us to determine its value in terms ofpand$$\kappa '$$${\kappa }^{\prime }$. It shows in particular that$$\hbox {CLE}_{\kappa '}$$${\text{CLE}}_{{\kappa }^{\prime }}$and$$\hbox {CLE}_{16/\kappa '}$$${\text{CLE}}_{16/{\kappa }^{\prime }}$are related via a continuum analog of the Edwards-Sokal coupling between$$\hbox {FK}_q$$${\text{FK}}_q$percolation and theq-state Potts model (which makes sense evenmore »for non-integerqbetween 1 and 4) if and only if$$q=4\cos ^2(4\pi / \kappa ')$$$q=4{cos}^2(4\pi /{\kappa }^{\prime })$. This provides further evidence for the long-standing belief that$$\hbox {CLE}_{\kappa '}$$${\text{CLE}}_{{\kappa }^{\prime }}$and$$\hbox {CLE}_{16/\kappa '}$$${\text{CLE}}_{16/{\kappa }^{\prime }}$represent the scaling limits of$$\hbox {FK}_q$$${\text{FK}}_q$percolation and theq-Potts model whenqand$$\kappa '$$${\kappa }^{\prime }$are related in this way. Another consequence of the formula for$$\rho (p,\kappa ')$$$\rho (p,{\kappa }^{\prime })$is the value of half-plane arm exponents for such divide-and-color models (a.k.a. fuzzy Potts models) that turn out to take a somewhat different form than the usual critical exponents for two-dimensional models.

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4. Approximate Unitary t-Designs by Short Random Quantum Circuits Using Nearest-Neighbor and Long-Range Gates

   https://doi.org/10.1007/s00220-023-04675-z  

   Harrow, Aram W. ; Mehraban, Saeed ( May 2023 , Communications in Mathematical Physics)

   We prove that$${{\,\textrm{poly}\,}}(t) \cdot n^{1/D}$$$\text{poly}\left(t\right)·n^{1/D}$-depth local random quantum circuits with two qudit nearest-neighbor gates on aD-dimensional lattice withnqudits are approximatet-designs in various measures. These include the “monomial” measure, meaning that the monomials of a random circuit from this family have expectation close to the value that would result from the Haar measure. Previously, the best bound was$${{\,\textrm{poly}\,}}(t)\cdot n$$$\text{poly}\left(t\right)·n$due to Brandão–Harrow–Horodecki (Commun Math Phys 346(2):397–434, 2016) for$$D=1$$$D=1$. We also improve the “scrambling” and “decoupling” bounds for spatially local random circuits due to Brown and Fawzi (Scrambling speed of random quantum circuits, 2012). One consequence of our result is that assuming the polynomial hierarchy ($${{\,\mathrm{\textsf{PH}}\,}}$$$\mathrm{PH}$) is infinite and that certain counting problems are$$\#{\textsf{P}}$$$\#P$-hard “on average”, sampling within total variation distance from these circuits is hard for classical computers. Previously, exact sampling from the outputs of even constant-depth quantum circuits was known to be hard for classical computers under these assumptions. However the standard strategy for extending this hardness result to approximate sampling requires the quantum circuits to have a property called “anti-concentration”, meaning roughly that the output has near-maximal entropy. Unitary 2-designs have the desired anti-concentration property. Our result improves the required depth for this level of anti-concentration from linear depthmore »to a sub-linear value, depending on the geometry of the interactions. This is relevant to a recent experiment by the Google Quantum AI group to perform such a sampling task with 53 qubits on a two-dimensional lattice (Arute in Nature 574(7779):505–510, 2019; Boixo et al. in Nate Phys 14(6):595–600, 2018) (and related experiments by USTC), and confirms their conjecture that$$O(\sqrt{n})$$$O\left(\sqrt{n}\right)$depth suffices for anti-concentration. The proof is based on a previous construction oft-designs by Brandão et al. (2016), an analysis of how approximate designs behave under composition, and an extension of the quasi-orthogonality of permutation operators developed by Brandão et al. (2016). Different versions of the approximate design condition correspond to different norms, and part of our contribution is to introduce the norm corresponding to anti-concentration and to establish equivalence between these various norms for low-depth circuits. For random circuits with long-range gates, we use different methods to show that anti-concentration happens at circuit size$$O(n\ln ^2 n)$$$O\left(n{ln}^{2}n\right)$corresponding to depth$$O(\ln ^3 n)$$$O\left({ln}^{3}n\right)$. We also show a lower bound of$$\Omega (n \ln n)$$$\Omega (nlnn)$for the size of such circuit in this case. We also prove that anti-concentration is possible in depth$$O(\ln n \ln \ln n)$$$O(lnnlnlnn)$(size$$O(n \ln n \ln \ln n)$$$O(nlnnlnlnn)$) using a different model.

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5. Plasmonically enhanced mid-IR light source based on tunable spectrally and directionally selective thermal emission from nanopatterned graphene

   https://doi.org/10.1038/s41598-020-73582-3  

   Shabbir, Muhammad Waqas ; Leuenberger, Michael N. ( October 2020 , Scientific Reports)

   We present a proof of concept for a spectrally selective thermal mid-IR source based on nanopatterned graphene (NPG) with a typical mobility of CVD-grown graphene (up to 3000$$\hbox {cm}^2\,\hbox {V}^{-1}\,\hbox {s}^{-1}$$${\text{cm}}^2{\text{V}}^{-1}{\text{s}}^{-1}$), ensuring scalability to large areas. For that, we solve the electrostatic problem of a conducting hyperboloid with an elliptical wormhole in the presence of anin-planeelectric field. The localized surface plasmons (LSPs) on the NPG sheet, partially hybridized with graphene phonons and surface phonons of the neighboring materials, allow for the control and tuning of the thermal emission spectrum in the wavelength regime from$$\lambda =3$$$\lambda =3$to 12$$\upmu$$$\mu$m by adjusting the size of and distance between the circular holes in a hexagonal or square lattice structure. Most importantly, the LSPs along with an optical cavity increase the emittance of graphene from about 2.3% for pristine graphene to 80% for NPG, thereby outperforming state-of-the-art pristine graphene light sources operating in the near-infrared by at least a factor of 100. According to our COMSOL calculations, a maximum emission power per area of$$11\times 10^3$$$11\times {10}^3$W/$$\hbox {m}^2$$${\text{m}}^2$at$$T=2000$$$T=2000$K for a bias voltage of$$V=23$$$V=23$V is achieved by controlling the temperature of the hot electrons through the Joule heating. By generalizing Planck’s theory to any grey body and derivingmore »the completely general nonlocal fluctuation-dissipation theorem with nonlocal response of surface plasmons in the random phase approximation, we show that the coherence length of the graphene plasmons and the thermally emitted photons can be as large as 13$$\upmu$$$\mu$m and 150$$\upmu$$$\mu$m, respectively, providing the opportunity to create phased arrays made of nanoantennas represented by the holes in NPG. The spatial phase variation of the coherence allows for beamsteering of the thermal emission in the range between$$12^\circ$$${12}^{\circ }$and$$80^\circ$$${80}^{\circ }$by tuning the Fermi energy between$$E_F=1.0$$$E_F=1.0$eV and$$E_F=0.25$$$E_F=0.25$eV through the gate voltage. Our analysis of the nonlocal hydrodynamic response leads to the conjecture that the diffusion length and viscosity in graphene are frequency-dependent. Using finite-difference time domain calculations, coupled mode theory, and RPA, we develop the model of a mid-IR light source based on NPG, which will pave the way to graphene-based optical mid-IR communication, mid-IR color displays, mid-IR spectroscopy, and virus detection.

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