Mastodawn

So as another enticement to my join class (from anywhere), I think this story serves as a poignant counterpoint to the way science is often done today. Whereas AI boosters claim we can throw data at algorithms and get "all of physics" (Altman) to pop out, Einstein's work in this year shows the power of deductive reasoning from assumed principles.

What we get to see in these papers is the work of an extremely creative mind. He sought unities and symmetries. These led him to construct simple stories that explained seemingly disparate phenomena better than the prevailing notions that were over-optimizing on smaller parts of the picture. I think this has lessons for us today in this world of constantly seeking more and bigger.

Aside from the papers, I'm excited to riff on his philosophical writings with our second faculty, who is an expert in German philosophy of the period, particularly Arendt and the Frankfurt School. Lots to say about induction, deduction, thinking, experience, and materialism. This is going to be a special class, and I don't want people to miss out. Signups are open, class starts Wednesday. Hope to see some of you!

https://thebrooklyninstitute.com/items/courses/new-york/albert-einstein-revolutions-in-physics/

#Einstein #physics #philosophy #relativity #quantum #StatMech

Albert Einstein: Revolutions in Physics

In quick succession in 1905, Albert Einstein—then an unprepossessing patent examiner in Bern, Switzerland—published four papers that would shake the foundations of contemporary physics and force a reconstruction, still unsettled to this day, of its basic notions of space, time, mass, energy, light, and matter. One of these, on Brownian motion, proved the reality of […]

Brooklyn Institute for Social Research

Alfred Jan 16

So 1905 was a good year for Einstein. So good that the centenary year was declared the World Year of Physics—not just of Einstein! This year marks 120 years since his annus mirabilis—his miraculous year. The papers he published would revolutionize how physicists think about matter, light, space, time, energy, even reality itself. How did all this come about in a single year—from a random upstart that the physics establishment had largely rejected, no less? What was unique in his philosophical inclinations that allowed him to perform this feat? Why were his theoretical arguments convincing? And honestly, how much help did he get?

That's what my next class will be about. Just four weeks, online, starting on the 29th, with readings to discuss history, philosophy, scientific context, impact, and legacy. I'll also walk us through the papers themselves. I think there are lessons today around intellectual honesty, cults of personality, and scientism (uncritical belief in science). Young scientists especially may find inspiration in the clarity of Einstein's thinking. Sign ups are slow this time around, so if you can't join yourself, spreading the word will help me out. Thanks!

https://thebrooklyninstitute.com/items/courses/new-york/albert-einstein-revolutions-in-physics/

#Einstein #physics #philosophy #relativity #quantum #StatMech

Albert Einstein: Revolutions in Physics

Brooklyn Institute for Social Research

Mike Tyka Aug 3, 2023

#statmech

|Ðr⟩⊕|JθΣħμαħ⟩⊗|Hεατħ⟩Jul 4, 2023

A question for the #CondMat and #StatMech communities here:

What are the possible routes for breaking integrability in a 1D chain of spinless fermions? Obviously one could do so with very strong interactions or perhaps longer-range hopping terms, but are these the only possible ways of breaking integrability in such a system?

|Ðr⟩⊕|JθΣħμαħ⟩⊗|Hεατħ⟩Jun 9, 2023

Today's #arXivsummary: https://arxiv.org/abs/2306.04682 by Singh et. al. Authors show that ensembles of initial states in anisotropic integrable spin chains with quasi-long range correlations lead to superdiffusive spin transport with a tunable dynamical exponent. Theoretical prediction provided for dynamical critical exponent. #CondMat #StatMech #arXiv_2306_04682

Tunable superdiffusion in integrable spin chains using correlated initial states

Although integrable spin chains only host ballistically propagating particles they can still feature diffusive spin transport. This diffusive spin transport originates from quasiparticle charge fluctuations inherited from the initial state's magnetization Gaussian fluctuations. We show that ensembles of initial states with quasi-long range correlations lead to superdiffusive spin transport with a tunable dynamical exponent. We substantiate our prediction with numerical simulations and explain how deviations arise from finite time and finite size effects.

arXiv.org

|Ðr⟩⊕|JθΣħμαħ⟩⊗|Hεατħ⟩Jun 7, 2023

Today's #arXivsummary: https://arxiv.org/abs/2306.03142 by Leo Radzihovsky. Chapter to be published in World Scientific, as "50 years of the renormalization group", dedicated to the memory of Michael E. Fisher. Novel ordered states of “critical matter” reviewed which exhibit strongly fluctuating universal power-law orders, controlled by an infrared attractive, non-Gaussian fixed point. #CondMat #StatMech #arXiv_2306_03142

Critical Matter

As part of a chapter for a book titled "50 years of the renormalization group", dedicated to the memory of Michael E. Fisher, edited by Amnon Aharony, Ora Entin-Wohlman, David Huse, and Leo Radzihovsky, I review a class of novel ordered states of "critical matter", that exhibit strongly fluctuating universal power-law orders, controlled by an infra-red attractive, non-Gaussian fixed point. I will illustrate how RG methods pioneered by Wilson and Fisher can be used to deduce critical phenomenology of such critical phases, resembling that of a critical point of second order phase transitions, but requiring no fine tuning.

arXiv.org

|Ðr⟩⊕|JθΣħμαħ⟩⊗|Hεατħ⟩Apr 11, 2023

Today's #arXivsummary: https://arxiv.org/abs/2304.03818 by Kassan-Ogly & Zarubin. Authors utilize a Kramers-Wannier transfer matrix method to study the frustration properties of the Ising model on a decorated triangular lattice with an arbitrary number of decorating spins on all lattice bonds. Entropy, heat capacity, and spontaneous magnetization found. #CondMat #StatMech #arXiv_2304_03818

Frustrations on decorated triangular lattice in Ising model

We study the frustration properties of the Ising model on a decorated triangular lattice with an arbitrary number of decorating spins on all lattice bonds in the framework of an exact analytical approach based on the Kramers--Wannier transfer matrix method. Expressions for the entropy, heat capacity, and spontaneous magnetization of the lattice are obtained, including the residual (zero-temperature) entropy and residual (zero-temperature) spontaneous magnetization of the system. The existence of magnetic frustrations in such a model and their influence on the behavior of the thermodynamic functions of the system are shown. The new and most important result of our study is related to the description of the possible coexistence of frustrations and long-range magnetic order in partially ordered spin systems.

arXiv.org

|Ðr⟩⊕|JθΣħμαħ⟩⊗|Hεατħ⟩Mar 27, 2023

Today's #arXivsummary: https://arxiv.org/abs/2303.14140 by Iubini et. al. Authors study nonequilibrium steady states of a one-dimensional stochastic model. When steadily maintained out-of-equilibrium, coupled transport exhibited which is studied within linear response theory. Onsager coefficients satisfy an exact scaling relationship. #arXivsummary #CondMat #StatMech

Onsager coefficients in a coupled-transport model displaying a condensation transition

We study nonequilibrium steady states of a one-dimensional stochastic model, originally introduced as an approximation of the Discrete Nonlinear Schrödinger equation. This model is characterized by two conserved quantities, namely mass and energy; it displays a ``normal", homogeneous phase, separated by a condensed (negative-temperature) phase, where a macroscopic fraction of energy is localized on a single lattice site. When steadily maintained out of equilibrium by external reservoirs, the system exhibits coupled transport herein studied within the framework of linear response theory. We find that the Onsager coefficients satisfy an exact scaling relationship, which allows reducing their dependence on the thermodynamic variables to that on the energy density for unitary mass density. We also determine the structure of the nonequilibrium steady states in proximity of the critical line, proving the existence of paths which partially enter the condensed region. This phenomenon is a consequence of the Joule effect: the temperature increase induced by the mass current is so strong as to drive the system to negative temperatures. Finally, since the model attains a diverging temperature at finite energy, in such a limit the energy-mass conversion efficiency reaches the ideal Carnot value.

arXiv.org

|Ðr⟩⊕|JθΣħμαħ⟩⊗|Hεατħ⟩Mar 20, 2023

Today's #arXivsummary: https://arxiv.org/abs/2303.09573 by Stahl et. al. Authors examine the hydrodynamics of systems with spontaneously broken multipolar symmetries using systematic effective field theory. In absence of any SSB, quartic subdiffusion found. With both charge and dipole symmetries broken, quadratically propagating (and quartically subdiffusing) mode found. #CondMat #StatMech #arXiv_2303_09573

Fracton superfluid hydrodynamics

We examine the hydrodynamics of systems with spontaneously broken multipolar symmetries using a systematic effective field theory. We focus on the simplest non-trivial setting: a system with charge and dipole symmetry, but without momentum conservation. When no symmetries are broken, our formalism reproduces the quartic subdiffusion ($ω\sim -i k^4$) characteristic of `fracton hydrodynamics' with conserved dipole moment. Our formalism also captures spontaneous breaking of charge and/or dipole symmetry. When charge symmetry is spontaneously broken, the hydrodynamic modes are quadratically propagating and quartically relaxing ($ω\sim \pm k^2 - ik^4$). When the dipole symmetry is spontaneously broken but the charge symmetry is preserved, then we find quadratically relaxing (diffusive) transverse modes, plus another mode which depending on parameters may be either purely diffusive ($ω\sim -i k^2$) or quadratically propagating and quadratically relaxing ($ω\sim \pm k^2 -i k^2$). Our work provides concrete predictions that may be tested in near-term cold atom experiments, and also lays out a general framework that may be applied to study systems with spontaneously broken multipolar symmetries.

arXiv.org

|Ðr⟩⊕|JθΣħμαħ⟩⊗|Hεατħ⟩Mar 17, 2023

Today's #arXivsummary: https://arxiv.org/abs/2303.08835 by Ouvry & Polychronakos. Authors introduce inclusion statistics, where particles tend to coalesce more than ordinary bosons. Lowest space dimension in which particles condense in absence of potentials is d=2. Critical temperature increases with stronger inclusion. #CondMat #StatMech #arXiv_2303_08835

Inclusion statistics and particle condensation in 2 dimensions

We propose a new type of quantum statistics, which we call inclusion statistics, in which particles tend to coalesce more than ordinary bosons. Inclusion statistics is defined in analogy with exclusion statistics, in which statistical exclusion is stronger than in Fermi statistics, but now extrapolating beyond Bose statistics, resulting in statistical inclusion. A consequence of inclusion statistics is that the lowest space dimension in which particles can condense in the absence of potentials is $d=2$, unlike $d=3$ for the usual Bose-Einstein condensation. This reduction in the dimension happens for any inclusion stronger than bosons, and the critical temperature increases with stronger inclusion. Possible physical realizations of inclusion statistics involving attractive interactions between bosons may be experimentally achievable.

arXiv.org