RECORD
Thermodynamic formalism and anomalous transport in 1D semiclassical Bose-Hubbard chain
Quantum Physics · Submitted 28 Dec 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This encapsulates the fact that in both slow- and fast-chaos regime both the anomalous and the normal diffusion can be seen (though at different times).
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We analyze the time-dependent free energy functionals of the semiclassical one-dimensional Bose-Hubbard chain. We first review the weakly chaotic dynamics and the consequent early-time anomalous diffusion in the system. The anomalous diffusion is robust, appears with strictly quantized coefficients, and persists even for very long chains (more than hundred sites), crossing over to normal diffusion at late times. We identify fast (angle) and slow (action) variables and thus consider annealed and quenched partition functions, corresponding to fixing the actions and integrating over the actions, respectively. We observe the leading quantum effects in the annealed free energy, whereas the quenched energy is undefined in the thermodynamic limit, signaling the absence of thermodynamic equilibrium in the quenched regime. But already the leading correction away from the quenched regime reproduces the annealed partition function exactly. This encapsulates the fact that in both slow- and fast-chaos regime both the anomalous and the normal diffusion can be seen (though at different times).
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We analyze the time-dependent free energy functionals of the semiclassical one-dimensional Bose-Hubbard chain. | contribution 0.99 | 0.91 | 0.04 | asserted 0.81 |
| s1 | We first review the weakly chaotic dynamics and the consequent early-time anomalous diffusion in the system. | background 0.70 | 0.26 | 0.06 | asserted 0.86 |
| s2 | The anomalous diffusion is robust, appears with strictly quantized coefficients, and persists even for very long chains (more than hundred sites), crossing over to normal diffusion at late times. | result 0.99 | 0.74 | 0.33 | asserted 1.00 |
| s3 | We identify fast (angle) and slow (action) variables and thus consider annealed and quenched partition functions, corresponding to fixing the actions and integrating over the actions, respectively. | method 0.92 | 0.82 | 0.05 | asserted 0.99 |
| s4 | We observe the leading quantum effects in the annealed free energy, whereas the quenched energy is undefined in the thermodynamic limit, signaling the absence of thermodynamic equilibrium in the quenched regime. | result 0.95 | 0.91 | 0.22 | asserted 1.00 |
| s5 | But already the leading correction away from the quenched regime reproduces the annealed partition function exactly. | result 0.94 | 0.89 | 0.17 | asserted 1.00 |
| s6 | This encapsulates the fact that in both slow- and fast-chaos regime both the anomalous and the normal diffusion can be seen (though at different times). | interpretation 0.99 | 0.65 | 0.29 | asserted 0.94 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We analyze the time-dependent free energy functionals of the semiclassical one-dimensional Bose-Hubbard chain. We first review the weakly chaotic dynamics and the consequent early-time anomalous diffusion in the system. The anomalous diffusion is robust, appears with strictly quantized coefficients, and persists even for very long chains (more than hundred sites), crossing over to normal diffusion at late times. We identify fast (angle) and slow (action) variables and thus consider annealed and quenched partition functions, corresponding to fixing the actions and integrating over the actions, respectively. We observe the leading quantum effects in the annealed free energy, whereas the quenched energy is undefined in the thermodynamic limit, signaling the absence of thermodynamic equilibrium in the quenched regime. But already the leading correction away from the quenched regime reproduces the annealed partition function exactly. This encapsulates the fact that in both slow- and fast-chaos regime both the anomalous and the normal diffusion can be seen (though at different times).
Human review
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 20 sentences without a confident label
Compares with 1 paper
-
Assuming that the above results make some sense for finite $L$, we note that the heat capacity now decreases with temperature as $1/T^2$, which is unexpectedly consistent with the results of [ref] , obtained without assuming the semiclassical approximation.
Double-peak specific heat anomaly and correlations in the Bose-Hubbard model · Quenched free energy · 0.97
Cites as background 9 papers
-
The vast and interesting phenomenology of cold atom systems [ref] , the universal behavior of theoretical models such as the SYK model [ref] , and novel indicators of quantum dynamics such as OTOC [ref] and Krylov complexity [ref] have led to resurgent interest in quantum chaos.
Black holes and the butterfly effect · Introduction · 1.00
-
The vast and interesting phenomenology of cold atom systems [ref] , the universal behavior of theoretical models such as the SYK model [ref] , and novel indicators of quantum dynamics such as OTOC [ref] and Krylov complexity [ref] have led to resurgent interest in quantum chaos.
A bound on chaos · Introduction · 1.00
-
The vast and interesting phenomenology of cold atom systems [ref] , the universal behavior of theoretical models such as the SYK model [ref] , and novel indicators of quantum dynamics such as OTOC [ref] and Krylov complexity [ref] have led to resurgent interest in quantum chaos.
Comments on the Sachdev-Ye-Kitaev model · Introduction · 1.00
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.