Article
Multidisciplinary Sciences
Jiaqi Cai, Eric Anderson, Chong Wang, Xiaowei Zhang, Xiaoyu Liu, William Holtzmann, Yinong Zhang, Fengren Fan, Takashi Taniguchi, Kenji Watanabe, Ying Ran, Ting Cao, Liang Fu, Di Xiao, Wang Yao, Xiaodong Xu
Summary: This study reports experimental evidence of fractional quantum anomalous Hall (FQAH) states in twisted MoTe2 bilayers. By using magnetic circular dichroism measurements and trion photoluminescence as a sensor, the researchers demonstrate the presence of FQAH states by observing the corresponding dispersion curves and linear shifts. These topological states can be electrically driven into topologically trivial states and provide a platform for exploring fractional excitations.
Article
Multidisciplinary Sciences
Daniel Shaffer, Jian Wang, Luiz H. Santos
Summary: In this work, we demonstrate through a renormalization group analysis that the combination of repulsive interactions and a tunable manifold of Van Hove singularities provides a new mechanism for driving unconventional superconductivity in Hofstadter bands. Our findings establish Hofstadter quantum materials like moire heterostructures as promising platforms for realizing novel reentrant Hofstadter superconductors.
NATURE COMMUNICATIONS
(2022)
Article
Physics, Multidisciplinary
Vidhi Shingla, Haoyun Huang, Ashwani Kumar, Loren N. Pfeiffer, Kenneth W. West, Kirk W. Baldwin, Gabor A. Csathy
Summary: Composite fermions can form bubbles that order into a lattice. The re-entrance of the fractional quantum Hall effect is associated with a bubble phase with two composite fermion quasiparticles per bubble. This observation demonstrates the existence of a new class of strongly correlated topological phases driven by clustering and charge ordering of emergent quasiparticles.
Article
Multidisciplinary Sciences
Yonglong Xie, Andrew T. Pierce, Jeong Min Park, Daniel E. Parker, Eslam Khalaf, Patrick Ledwith, Yuan Cao, Seung Hwan Lee, Shaowen Chen, Patrick R. Forrester, Kenji Watanabe, Takashi Taniguchi, Ashvin Vishwanath, Pablo Jarillo-Herrero, Amir Yacoby
Summary: Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states and have been recently observed in magic-angle twisted BLG at low magnetic field. The appearance of these states at 5 T is accompanied by the disappearance of nearby topologically trivial charge density wave states.
Article
Physics, Multidisciplinary
A. McDonald, A. A. Clerk
Summary: In this paper, we demonstrate how the presence of continuous weak symmetry can be used to analytically diagonalize the Liouvillian of a class of Markovian dissipative systems with strong interactions or nonlinearity. This method enables an exact description of the full dynamics and dissipative spectrum, providing a powerful new tool for the study of complex driven-dissipative quantum systems.
PHYSICAL REVIEW LETTERS
(2022)
Article
Materials Science, Multidisciplinary
Haleh Tajadodi, Zareen A. Khan, Ateeq ur Rehman Irshad, J. F. Gomez-Aguilar, Aziz Khan, Hasib Khan
Summary: This article discusses how to formulate exact solutions of the time fractional DBM equation, Sinh-Gordon equation and Liouville equation using the simplest equation method in the context of conformable fractional derivatives. By transforming the original equations into nonlinear ODEs, the method provides a simple yet effective approach for solving FOPDEs.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Esteban Gonzalez, Genly Leon, Guillermo Fernandez-Anaya
Summary: This paper investigates exact solutions of cosmological interest in fractional cosmology. Given mu and w, specific exact power-law solutions are presented. The general solution of the Riccati Equation is discussed and the free parameters are estimated using cosmological data. Best-fit values for the free parameters are obtained through analyses with type Ia supernova data and observational Hubble parameter data. The results suggest that the parameter region with mu > 2 is not ruled out by observations, indicating the potential of fractional cosmology in providing accelerated solutions without matter.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
V. F. Morales-Delgado, M. A. Taneco-Hernandez, Cruz Vargas-De-Leon, J. F. Gomez-Aguilar
Summary: The aim of this paper is to mathematically analyze the administration of drugs through continuous intravenous infusion or oral dose. We use fractional-order mammillary-type models to describe the anomalous dynamics of concentration exchange, considering constant input rates, power-law types, and discrete oral doses. A general analysis strategy is developed, providing closed-form analytical solutions in terms of the multivariate Mittag-Leffler function. Numerical simulations with literature parameters are performed.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Multidisciplinary
Huajun Zeng, Yuxia Wang, Min Xiao, Ying Wang
Summary: This paper studies famous fractional wave equations, such as the fractional KdV-Burgers equation and the fractional approximate long water wave equation, using a modified tanh-function method. It provides a detailed solving process, and the obtained exact solutions rigorously explain new solitons phenomena. This paper offers a new window for studying fractional solitons.
FRONTIERS IN PHYSICS
(2023)
Article
Engineering, Mechanical
Alessandra Jannelli, Maria Paola Speciale
Summary: In this paper, a two-dimensional time-fractional diffusion-reaction equation involving the Riemann-Liouville derivative is studied using a combination of Lie symmetry analysis and numerical methods, leading to exact and numerical solutions. The target equation is transformed into a new one-dimensional time-fractional differential equation through Lie transformations, and exact and numerical solutions are obtained by solving the reduced fractional partial differential equation. Numerical solutions are determined by introducing the Caputo definition fractional derivative and using an implicit classical numerical method, with comparisons made between the numerical and exact solutions.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
R. Najafi, F. Bahrami, S. Shahmorad
Summary: This study proposes the concept of compatibility between fractional-order differential equations and integer-order ones, and derives exact solutions by imposing compatibility criteria.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Aysegul Dascioglu, Sevil Culha Unal
Summary: The Kawahara equation is a model of capillary-gravity water wave and plasma waves. A direct method based on the Jacobi elliptic functions is presented to get analytical solutions of the space-time fractional Kawahara equation. New exact solutions are obtained for a nonlinear ordinary differential equation, which appears as an auxiliary equation for solving many partial differential equations. By solving this auxiliary equation, the solutions of the Duffing equation can also be found.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Mathematics, Applied
Li Liu, Qixiang Dong, Gang Li
Summary: In this paper, we study the exact solutions of a class of fractional delay differential equations and introduce two novel matrix functions. The explicit solutions and analytical representations for linear homogeneous and inhomogeneous equations are obtained using undetermined coefficients and the Laplace transform, respectively.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2022)
Article
Mathematics, Applied
Li Liu, Qixiang Dong, Gang Li
Summary: In this study, we obtain the exact solutions to higher fractional-order nonhomogeneous delayed differential equations with Caputo-type fractional derivative by using newly defined generalized delayed Mittag-Leffler matrix functions. We also propose criteria on the finite time stability of these equations. The theoretical results are validated through an illustrative example.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Abass H. Abdel Kader, Mohamed S. Abdel Latif, Dumitru Baleanu
Summary: This paper investigates the exact solutions of a nonlinear variable coefficients time fractional biological population model using the invariant subspace method. Subspaces with dimensions one, two, and three are derived for certain cases of the variable coefficients, leading to exact solutions in some cases.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Physics, Multidisciplinary
Glenn Wagner, Dung X. Nguyen, Steven H. Simon
PHYSICAL REVIEW LETTERS
(2020)
Article
Physics, Multidisciplinary
Felix Flicker, Steven H. Simon, S. A. Parameswaran
Article
Physics, Multidisciplinary
Yves H. Kwan, Yichen Hu, Steven H. Simon, S. A. Parameswaran
Summary: The study reveals the topological features of neutral particle-hole pair excitations and their impact on the bound states in correlated QAH insulators. This results in the formation of topological exciton bands with robust features. The research also applies these ideas to broken-symmetry spontaneous QAH insulators in magic-angle twisted bilayer graphene with substrate alignment.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Maja D. Bachmann, Aaron L. Sharpe, Graham Baker, Arthur W. Barnard, Carsten Putzke, Thomas Scaffidi, Nabhanila Nandi, Philippa H. McGuinness, Elina Zhakina, Michal Moravec, Seunghyun Khim, Markus Konig, David Goldhaber-Gordon, Douglas A. Bonn, Andrew P. Mackenzie, Philip J. W. Moll
Summary: In a finite crystal, the shape of the crystal breaks the point-group symmetry, leading to changes in the material properties. Experimental results show that the strongly facetted Fermi surface and long quasiparticle mean free path in microstructures of PdCoO2 result in an in-plane resistivity anisotropy, which is forbidden by symmetry on an infinite hexagonal lattice. The direction of the narrow channel is identified as the source of symmetry breaking.
Article
Multidisciplinary Sciences
Fabian Jerzembeck, Henrik S. Roising, Alexander Steppke, Helge Rosner, Dmitry A. Sokolov, Naoki Kikugawa, Thomas Scaffidi, Steven H. Simon, Andrew P. Mackenzie, Clifford W. Hicks
Summary: Applying in-plane uniaxial pressure can dramatically change the electronic structure of strongly correlated low-dimensional systems, and using pressure along the c axis can provide even stronger control over the quasi-two-dimensional structure. In the superconductor Sr2RuO4, in-plane strain enhances Tc and Hc2, but the effect of out-of-plane strain has not been studied.
NATURE COMMUNICATIONS
(2022)
Article
Multidisciplinary Sciences
C. Kumar, J. Birkbeck, J. A. Sulpizio, D. Perello, T. Taniguchi, K. Watanabe, O. Reuven, T. Scaffidi, Ady Stern, A. K. Geim, S. Ilani
Summary: Recent research has shown that hydrodynamic electronic phenomena can transcend the fundamental limitations of ballistic electrons, with important implications for fundamental science and future technologies. High-mobility graphene Corbino disk devices were used to image single-electron-transistor electronic flow, revealing the elimination of bulk Landauer-Sharvin resistance by electron hydrodynamics. This study highlights the potential of electronic fluids to revolutionize electronic conduction.
Article
Physics, Multidisciplinary
Ady Stern, Thomas Scaffidi, Oren Reuven, Chandan Kumar, John Birkbeck, Shahal Ilani
Summary: Recent research has shown that by choosing the proper device geometry, it is possible to eliminate Landauer-Sharvin resistance in an electronic system through electron hydrodynamics. The dynamics of electrons flowing in channels terminating within the sample play a crucial role in this effect. Contrary to ohmic electrons, the resistance of hydrodynamic electrons can decrease with the length of a device with a given width.
PHYSICAL REVIEW LETTERS
(2022)
Correction
Materials Science, Multidisciplinary
Maxime Dupont, Snir Gazit, Thomas Scaffidi
Article
Materials Science, Multidisciplinary
Thomas Scaffidi
Summary: Based on a weak coupling calculation, it is shown that accidental degeneracy occurs between even- and odd-parity superconductivity in the quasi-one-dimensional (1D) limit of the repulsive Hubbard model on the square lattice. It is proposed that this effect may be relevant to the quasi-1D orbitals Ru dzx and dzy of Sr2RuO4, resulting in a gap of the form Aeven + iAodd, which could help reconcile several experimental results.
Article
Materials Science, Multidisciplinary
Jack H. Farrell, Nicolas Grisouard, Thomas Scaffidi
Summary: In this study, we investigate the radial flow in a Corbino disk and find that this geometry significantly enhances the Dyakonov-Shur (DS) instability, leading to higher generated power. This is directly relevant to current efforts to detect the experimentally elusive phenomenon of hydrodynamic electron flows.
Article
Materials Science, Multidisciplinary
Maxime Dupont, Snir Gazit, Thomas Scaffidi
Summary: Using quantum Monte Carlo simulations, we mapped out the phase diagram of Hamiltonians transitioning between trivial and nontrivial bosonic symmetry-protected topological phases, finding an intermediate phase where the protecting symmetry is spontaneously broken. Various magnetic orders on the triangular lattice were identified, and critical properties were determined through finite-size scaling analysis, with possible scenarios regarding the nature of phase transitions discussed.
Article
Physics, Multidisciplinary
Arijit Haldar, Omid Tavakol, Thomas Scaffidi
Summary: In the context of q-local Hamiltonians, simple variational states can have energy a finite fraction of the ground-state energy, with product states being more successful in bosonic models than Gaussian states in fermionic cases like the Sachdev-Ye-Kitaev (SYK) model. A new class of wave functions inspired by the variational coupled cluster algorithm is proposed for SYK models, with a study focusing on energy, two-point correlators, and entanglement properties using a static (0+0)-dimensional large-N field theory. Importantly, a finite disorder-averaged approximation ratio between variational and ground-state energy is demonstrated for the SYK model with q = 4, and variational states accurately describe spontaneous symmetry breaking in a related two-flavor SYK model.
PHYSICAL REVIEW RESEARCH
(2021)
Article
Optics
Xiangyu Cao, Thomas Scaffidi
Summary: Recent research has shown that scrambled information can be partially recovered through time-reversed evolution even after being damaged by an intruder. The presence of classical chaos does not completely prevent information recovery, but rather leads to a reduction in the recovery ratio. Furthermore, decoherence (i.e., entanglement with the intruder) limits the recovery process, with an upper bound on the recovery ratio determined by the entangling power of the intruder's actions.
Article
Materials Science, Multidisciplinary
Dung X. Nguyen, Glenn Wagner, Steven H. Simon
Article
Materials Science, Multidisciplinary
Steven H. Simon, Matteo Ippoliti, Michael P. Zaletel, Edward H. Rezayi