Fetching the paper…
Reading the bibliography…
Pattern formation is a ubiquitous phenomenon observed in nonlinear and out-of-equilibrium systems.
P. A. M. Dirac, “Forms of Relativistic Dynamics,” Rev. Mod. Phys. 21
1949
Earlier work this paper cites.
A. M. Turing, “The chemical basis of morphogenesis,” Phil. Trans. Roy. Soc. London Series B, Bio. Sci. 237
1952
Earlier work this paper cites.
R. P. Huebener and J. R. Clem, “Magnetic flux structures in superconductors—a conference summary,” Rev. Mod. Phys. 46
1974
Earlier work this paper cites.
R. E. Rosensweig, M. Zahn, and R. Shumovich, “Labyrinthine instability in magnetic and dielectric fluids,” J. Magnetism and Magnetic Materials 39
1983
Earlier work this paper cites.
D. G. Ravenhall, C. J. Pethick, and J. R. Wilson, “Structure of Matter below Nuclear Saturation Density,” Phys. Rev. Lett. 50
1983
Earlier work this paper cites.
K. Perlin, “An Image Synthesizer,” SIGGRAPH Comp. Graph. 19
1985
Earlier work this paper cites.
Q. Ouyang and H. L. Swinney, “Transition from a uniform state to hexagonal and striped Turing patterns,” Nature (London) 352
1991
Earlier work this paper cites.
S. Sachdev, “Kagomé- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons,” Phys. Rev. B 45
1992
Earlier work this paper cites.
A. J. Dickstein, S. Erramilli, R. E. Goldstein, D. P. Jackson, and S. A. Langer, “Labyrinthine Pattern Formation in Magnetic Fluids,” Science 261
1993
Earlier work this paper cites.
E. Ciaramella, M. Tamburrini, and E. Santamato, “Talbot assisted hexagonal beam patterning in a thin liquid crystal film with a single feedback mirror at negative distance,” Appl. Phys. Lett. 63
1993
Earlier work this paper cites.
M. C. Cross and P. C. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65
1993
Earlier work this paper cites.
G. Ahlers, L. I. Berge, and D. S. Cannell, “Thermal convection in the presence of a first-order phase change,” Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, “Spiral defect chaos in large aspect ratio Rayleigh-Bénard convection,” Phys. Rev. Lett. 71
1993
Earlier work this paper cites.
D. P. Jackson, R. E. Goldstein, and A. O. Cebers, “Hydrodynamics of fingering instabilities in dipolar fluids,” Phys. Rev. E 50
1994
Earlier work this paper cites.
W. S. Edwards and S. Fauve, “Patterns and quasi-patterns in the Faraday experiment,” J. Fluid Mech. 278
1994
Earlier work this paper cites.
M. Seul and D. Andelman, “Domain Shapes and Patterns: The Phenomenology of Modulated Phases,” 267
1995
Earlier work this paper cites.
T. Ackemann, Yu. A. Logvin, A. Heuer, and W. Lange, “Transition between positive and negative hexagons in optical pattern formation,” Phys. Rev. Lett. 75
1995
Earlier work this paper cites.
C. J. Pethick and D. G. Ravenhall, “Matter at Large Neutron Excess and the Physics of Neutron-Star Crusts,” Annu. Rev. Nuc. Part. Sci. 45
1995
Earlier work this paper cites.
R. E. Rosensweig, Ferrohydrodynamics , Dover Books on Physics (Dover Publications, 1997)
1997
Earlier work this paper cites.
E. Florence, F. Cyrille, J.-C. Bacri, and S. Neveu, “Macro-Organized Patterns in Ferrofluid Layer: Experimental Studies,” J. Phys. I France 7
1997
Earlier work this paper cites.
D. Han, Y. S. Kim, and M. E. Noz, “Jones-matrix formalism as a representation of the Lorentz group,” J. Opt. Soc. Am. A 14
1997
Earlier work this paper cites.
S. Grebenev, J. P. Toennies, and A. F. Vilesov, “Superfluidity Within a Small Helium-4 Cluster: The Microscopic Andronikashvili Experiment,” Science 279
1998
Earlier work this paper cites.
F.T. Arecchi, S. Boccaletti, and P. Ramazza, “Pattern formation and competition in nonlinear optics,” Physics Reports 318
1999
Earlier work this paper cites.
F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys. 71
1999
Earlier work this paper cites.
Krzysztof Góral, Kazimierz Rza¸żewski, and Tilman Pfau, “Bose-Einstein condensation with magnetic dipole-dipole forces,” Phys. Rev. A 61
2000
Earlier work this paper cites.
D. O’Dell, S. Giovanazzi, G. Kurizki, and V. M. Akulin, “Bose-Einstein Condensates with 1 / r 1/\mathit{r} Interatomic Attraction: Electromagnetically Induced “Gravity”,” Phys. Rev. Lett. 84
2000
Earlier work this paper cites.
F. Dalfovo and S. Stringari, “Helium nanodroplets and trapped Bose–Einstein condensates as prototypes of finite quantum fluids,” J. Chem. Phys. 115
2001
Earlier work this paper cites.
J. P. Toennies, A. F. Vilesov, and K. B. Whaley, “Superfluid Helium Droplets: An Ultracold Nanolaboratory,” Physics Today 54
2001
Earlier work this paper cites.
J. von Hardenberg, E. Meron, M. Shachak, and Y. Zarmi, “Diversity of Vegetation Patterns and Desertification,” Phys. Rev. Lett. 87
2001
Earlier work this paper cites.
A. Bulgac, “Dilute Quantum Droplets,” Phys. Rev. Lett. 89
2002
Earlier work this paper cites.
M. Le Berre, E. Ressayre, A. Tallet, Y. Pomeau, and L. Di Menza, “Example of a chaotic crystal: The labyrinth,” Phys. Rev. E 66
2002
Earlier work this paper cites.
K. Góral and L. Santos, “Ground state and elementary excitations of single and binary Bose-Einstein condensates of trapped dipolar gases,” Phys. Rev. A 66
2002
Earlier work this paper cites.
L. Santos, G. V. Shlyapnikov, and M. Lewenstein, “Roton-Maxon Spectrum and Stability of Trapped Dipolar Bose-Einstein Condensates,” Phys. Rev. Lett. 90
2003
Earlier work this paper cites.
M. Modugno, L. Pricoupenko, and Y. Castin, “Bose-Einstein condensates with a bent vortex in rotating traps,” Eur. Phys. J. D 22
2003
Earlier work this paper cites.
M. Bender, P.-H. Heenen, and P.-G. Reinhard, “Self-consistent mean-field models for nuclear structure,” Rev. Mod. Phys. 75
2003
Earlier work this paper cites.
K. B. W. Buckley, M. A. Metlitski, and A. R. Zhitnitsky, “Neutron Stars as Type-I Superconductors,” Phys. Rev. Lett. 92
2004
Earlier work this paper cites.
José A. Miranda and Enrique Alvarez-Lacalle, “Viscosity contrast effects on fingering formation in rotating hele-shaw flows,” Phys. Rev. E 72
2005
Earlier work this paper cites.
A. Cēbers, C. Gourdon, V. Jeudy, and T. Okada, “Normal-state bubbles and lamellae in type-I superconductors,” Phys. Rev. B 72
2005
Earlier work this paper cites.
I. H. Riedel, K. Kruse, and J. Howard, “A Self-Organized Vortex Array of Hydrodynamically Entrained Sperm Cells,” Science 309
2005
Earlier work this paper cites.
K. Nelissen, B. Partoens, and F. M. Peeters, “Bubble, stripe, and ring phases in a two-dimensional cluster with competing interactions,” Phys. Rev. E 71
2005
Earlier work this paper cites.
C. Eberlein, S. Giovanazzi, and D. H. J. O’Dell, “Exact solution of the Thomas-Fermi equation for a trapped Bose-Einstein condensate with dipole-dipole interactions,” Phys. Rev. A 71
2005
Earlier work this paper cites.
R. Schützhold, M. Uhlmann, Y. Xu, and U. R. Fischer, “Mean-Field Expansion in Bose–Einstein Condensates with Finite-Range Interactions,” Int. J. Mod. Phys. B 20
2006
Earlier work this paper cites.
S. Ronen, D. C. E. Bortolotti, and J. L. Bohn, “Bogoliubov modes of a dipolar condensate in a cylindrical trap,” Phys. Rev. A 74
2006
Earlier work this paper cites.
R. Prozorov, “Equilibrium Topology of the Intermediate State in Type-I Superconductors of Different Shapes,” Phys. Rev. Lett. 98
2007
Earlier work this paper cites.
T. Lahaye, T. Koch, B. Fröhlich, M. Fattori, J. Metz, A. Griesmaier, S. Giovanazzi, and T. Pfau, “Strong dipolar effects in a quantum ferrofluid,” Nature (London) 448
2007
Earlier work this paper cites.
N. V. Prokof’ev, “What makes a crystal supersolid?” Adv. Phys. 56
2007
Earlier work this paper cites.
S. Ronen, D. C. E. Bortolotti, and J. L. Bohn, “Radial and angular rotons in trapped dipolar gases,” Phys. Rev. Lett. 98
2007
Earlier work this paper cites.
O. Dutta and P. Meystre, “Ground-state structure and stability of dipolar condensates in anisotropic traps,” Phys. Rev. A 75
2007
Earlier work this paper cites.
A. Aftalion, X. Blanc, and R. L. Jerrard, “Nonclassical Rotational Inertia of a Supersolid,” Phys. Rev. Lett. 99
2007
Cited alongside, same era.
I. Papadopoulos, P. Wagner, G. Wunner, and J. Main, “Bose-Einstein condensates with attractive 1 / r 1/r interaction: The case of self-trapping,” Phys. Rev. A 76
2007
Cited alongside, same era.
R. Prozorov, A. F. Fidler, J. R. Hoberg, and P. C. Canfield, “Suprafroth in type-I superconductors,” Nat. Phys. 4
2008
Cited alongside, same era.
N. Chamel and P. Haensel, “Physics of Neutron Star Crusts,” Living Rev. Rel. 11
2008
Cited alongside, same era.
I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80
2008
Cited alongside, same era.
L. Chomaz, S. Baier, D. Petter, M. J. Mark, F. Wächtler, L. Santos, and F. Ferlaino, “Quantum-Fluctuation-Driven Crossover from a Dilute Bose-Einstein Condensate to a Macrodroplet in a Dipolar Quantum Fluid,” Phys. Rev. X 6
2016
Later among the works it cites.
D. Baillie, R. M. Wilson, R. N. Bisset, and P. B. Blakie, “Self-bound dipolar droplet: A localized matter wave in free space,” Phys. Rev. A 94
2016
Later among the works it cites.
H. Saito, “Path-Integral Monte Carlo Study on a Droplet of a Dipolar Bose–Einstein Condensate Stabilized by Quantum Fluctuation,” J. Phys. Soc. Jpn 85
2016
Later among the works it cites.
L.P. Pitaevskii and S. Stringari, Bose-Einstein Condensation and Superfluidity , International series of monographs on physics (Oxford University Press, 2016)
2016
Later among the works it cites.
S. Ostermann, F. Piazza, and H. Ritsch, “Spontaneous Crystallization of Light and Ultracold Atoms,” Phys. Rev. X 6
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A. J. Archer, C. Ionescu, D. Pini, and L. Reatto, “Theory for the phase behaviour of a colloidal fluid with competing interactions,” J. Phys. Cond. Mat. 20
2008
Cited alongside, same era.
Y. H. Liu, L. Y. Chew, and M. Y. Yu, “Self-assembly of complex structures in a two-dimensional system with competing interaction forces,” Phys. Rev. E 78
2008
Cited alongside, same era.
R. M. Wilson, S. Ronen, J. L. Bohn, and H. Pu, “Manifestations of the roton mode in dipolar bose-einstein condensates,” Phys. Rev. Lett. 100
2008
Cited alongside, same era.
T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, and M. Ueda, “ d d -Wave Collapse and Explosion of a Dipolar Bose-Einstein Condensate,” Phys. Rev. Lett. 101
2008
Cited alongside, same era.
T. Koch, T. Lahaye, J. Metz, B. Fröhlich, A. Griesmaier, and T. Pfau, “Stabilization of a purely dipolar quantum gas against collapse,” Nat. Phys. 4
2008
Cited alongside, same era.
D. Andelman and R. E. Rosensweig, “Modulated Phases: Review and Recent Results,” J. Phys. Chem. B 113
2009
Cited alongside, same era.
T. Lahaye, C. Menotti, L. Santos, M. Lewenstein, and T. Pfau, “The physics of dipolar bosonic quantum gases,” Rep. Prog. Phys. 72
2009
Cited alongside, same era.
2016
Later among the works it cites.
F. Wächtler and L. Santos, “Ground-state properties and elementary excitations of quantum droplets in dipolar Bose-Einstein condensates,” Phys. Rev. A 94
2016
Later among the works it cites.
R. N. Bisset, R. M. Wilson, D. Baillie, and P. B. Blakie, “Ground-state phase diagram of a dipolar condensate with quantum fluctuations,” Phys. Rev. A 94
2016
Later among the works it cites.
A. Zakinyan, E. Beketova, and Y. Dikansky, “Flows and instabilities of ferrofluids at the microscale,” Microfluidics and Nanofluidics 21
2017
Later among the works it cites.
F. Maucher, T. Pohl, W. Krolikowski, and S. Skupin, “Pattern formation in the nonlinear Schrödinger equation with competing nonlocal nonlinearities,” Optical Data Processing and Storage 3
2017
Later among the works it cites.
M. E. Caplan and C. J. Horowitz, “Colloquium: Astromaterial science and nuclear pasta,” Rev. Mod. Phys. 89
2017
Later among the works it cites.
D. Baillie, R. M. Wilson, and P. B. Blakie, “Collective Excitations of Self-Bound Droplets of a Dipolar Quantum Fluid,” Phys. Rev. Lett. 119
2017
Later among the works it cites.
M. Wenzel, F. Böttcher, T. Langen, I. Ferrier-Barbut, and T. Pfau, “Striped states in a many-body system of tilted dipoles,” Phys. Rev. A 96
2017
Later among the works it cites.
X. Antoine, A. Levitt, and Q. Tang, “Efficient spectral computation of the stationary states of rotating Bose–Einstein condensates by preconditioned nonlinear conjugate gradient methods,” J. Comp. Phys. 343
2017
Later among the works it cites.
F. Cinti and M. Boninsegni, “Classical and quantum filaments in the ground state of trapped dipolar Bose gases,” Phys. Rev. A 96
2017
Later among the works it cites.
Y.-C. Zhang, V. Walther, and T. Pohl, “Long-Range Interactions and Symmetry Breaking in Quantum Gases through Optical Feedback,” Phys. Rev. Lett. 121
2018
Later among the works it cites.
M. Wenzel, F. Böttcher, J.-N. Schmidt, M. Eisenmann, T. Langen, T. Pfau, and I. Ferrier-Barbut, “Anisotropic Superfluid Behavior of a Dipolar Bose-Einstein Condensate,” Phys. Rev. Lett. 121
2018
Later among the works it cites.
Ferrier-Barbut, I. and Pfau, T., “Quantum liquids get thin,” Science 359
2018
Later among the works it cites.
D. Baillie and P. B. Blakie, “Droplet Crystal Ground States of a Dipolar Bose Gas,” Phys. Rev. Lett. 121
2018
Later among the works it cites.
K.-T. Xi, T. Byrnes, and H. Saito, “Fingering instabilities and pattern formation in a two-component dipolar Bose-Einstein condensate,” Phys. Rev. A 97
2018
Later among the works it cites.
X. Antoine, Q. Tang, and Y. Zhang, “A Preconditioned Conjugated Gradient Method for Computing Ground States of Rotating Dipolar Bose-Einstein Condensates via Kernel Truncation Method for Dipole-Dipole Interaction Evaluation,” Comm. Comp. Phys. 24
2018
Later among the works it cites.
G. E. Astrakharchik and B. A. Malomed, “Dynamics of one-dimensional quantum droplets,” Phys. Rev. A 98
2018
Later among the works it cites.
I. Ferrier-Barbut, M. Wenzel, M. Schmitt, F. Böttcher, and T. Pfau, “Onset of a modulational instability in trapped dipolar Bose-Einstein condensates,” Phys. Rev. A 97
2018
Later among the works it cites.
L. Chomaz, R. M. W. van Bijnen, D. Petter, G. Faraoni, S. Baier, J. H. Becher, M. J. Mark, F. Wächtler, L. Santos, and F. Ferlaino, “Observation of roton mode population in a dipolar quantum gas,” Nat. Phys. 14
2018
Later among the works it cites.
Y. Kora and M. Boninsegni, “Patterned Supersolids in Dipolar Bose Systems,” J. Low Temp. Phys. 197
2019
Later among the works it cites.
I. Ferrier-Barbut, “Ultradilute Quantum Droplets,” Physics Today 72
2019
Later among the works it cites.
L. Chomaz, D. Petter, P. Ilzhöfer, G. Natale, A. Trautmann, C. Politi, G. Durastante, R. M. W. van Bijnen, A. Patscheider, M. Sohmen, M. J. Mark, and F. Ferlaino, “Long-Lived and Transient Supersolid Behaviors in Dipolar Quantum Gases,” Phys. Rev. X 9
2019
Later among the works it cites.
M. Guo, F. Böttcher, J. Hertkorn, J.-N. Schmidt, M. Wenzel, H. P. Büchler, T. Langen, and T. Pfau, “The low-energy Goldstone mode in a trapped dipolar supersolid,” Nature (London) 574
2019
Later among the works it cites.
G. Natale, R. M. W. van Bijnen, A. Patscheider, D. Petter, M. J. Mark, L. Chomaz, and F. Ferlaino, “Excitation Spectrum of a Trapped Dipolar Supersolid and Its Experimental Evidence,” Phys. Rev. Lett. 123
2019
Later among the works it cites.
J. Hertkorn, F. Böttcher, M. Guo, J.-N. Schmidt, T. Langen, H. P. Büchler, and T. Pfau, “Fate of the Amplitude Mode in a Trapped Dipolar Supersolid,” Phys. Rev. Lett. 123
2019
Later among the works it cites.
S. M. Roccuzzo and F. Ancilotto, “Supersolid behavior of a dipolar Bose-Einstein condensate confined in a tube,” Phys. Rev. A 99
2019
Later among the works it cites.
Y.-C. Zhang, F. Maucher, and T. Pohl, “Supersolidity around a critical point in dipolar Bose Einstein condensates,” Phys. Rev. Lett. 123
2019
Later among the works it cites.
V. Heinonen, K. J. Burns, and J. Dunkel, “Quantum hydrodynamics for supersolid crystals and quasicrystals,” Phys. Rev. A 99
2019
Later among the works it cites.
G. Baio, G. R. M. Robb, A. M. Yao, and G.-L. Oppo, “Optomechanical transport of cold atoms induced by structured light,” Phys. Rev. Research 2
2020
Later among the works it cites.
H. Hu and X.-J. Liu, “Collective excitations of a spherical ultradilute quantum droplet,” Phys. Rev. A 102
2020
Later among the works it cites.
Z.-H. Luo, W. Pang, B. Liu, Y.-Y. Li, and B. A. Malomed, “A new form of liquid matter: Quantum droplets,” Front. Phys. 16
2020
Later among the works it cites.
S. Pal, D. Baillie, and P. B. Blakie, “Excitations and number fluctuations in an elongated dipolar Bose-Einstein condensate,” Phys. Rev. A 102
2020
Later among the works it cites.
S. M. Roccuzzo, A. Gallemí, A. Recati, and S. Stringari, “Rotating a Supersolid Dipolar Gas,” Phys. Rev. Lett. 124
2020
Later among the works it cites.
A. Gallemí, S. M. Roccuzzo, S. Stringari, and A. Recati, “Quantized vortices in dipolar supersolid Bose-Einstein-condensed gases,” Phys. Rev. A 102
2020
Later among the works it cites.
S. Echeverría-Alar and M. G. Clerc, “Labyrinthine patterns transitions,” Phys. Rev. Research 2
2020
Later among the works it cites.
M. Tylutki, G. E. Astrakharchik, B. A. Malomed, and D. S. Petrov, “Collective excitations of a one-dimensional quantum droplet,” Phys. Rev. A 101
2020
Later among the works it cites.
G. Valtolina, K. Matsuda, W. G. Tobias, J.-R. Li, L. De Marco, and J. Ye, “Dipolar evaporation of reactive molecules to below the Fermi temperature,” Nature (London) 588
2020
Later among the works it cites.
F. Böttcher, J.-N. Schmidt, J. Hertkorn, K. S. H. Ng, S. D. Graham, M. Guo, T. Langen, and T. Pfau, “New states of matter with fine-tuned interactions: quantum droplets and dipolar supersolids,” Rep. Prog. Phys. 84
2021
Closest in time.
2021
Closest in time.
L. Tanzi, J. G. Maloberti, G. Biagioni, A. Fioretti, C. Gabbanini, and G. Modugno, “Evidence of superfluidity in a dipolar supersolid from nonclassical rotational inertia,” Science 371
2021
Closest in time.
P. Ilzhöfer, M. Sohmen, G. Durastante, C. Politi, A. Trautmann, G. Natale, G. Morpurgo, T. Giamarchi, L. Chomaz, M. J. Mark, and F. Ferlaino, “Phase coherence in out-of-equilibrium supersolid states of ultracold dipolar atoms,” Nat. Phys. (2021), https://doi.org/10.1038/s41567-020-01100-3
2021
Closest in time.
2021
Closest in time.