We study the photoinduced dynamics of the excitonic insulator in the two-orbital Hubbard model on the Penrose tiling by means of the time-dependent real-space mean-field approximation. We show that, with a single-cycle electric-field pulse, the bulk (spatially averaged) excitonic order parameter decreases in the Bardeen-Cooper-Schrieffer (BCS) regime, while it increases in the Bose-Einstein condensate (BEC) regime. This behavior is in common with the excitonic insulator in the square lattice reported previously. To explore the dynamics peculiar to the Penrose tiling, we examine the coordination number dependence of observables and analyze the perpendicular space. In the BEC regime, characteristic oscillations of the electron number at each site are induced by the pulse, which are not observed in normal crystals with single coordination number. On the other hand, the dynamics in the BCS regime is characterized by drastic change in the spatial pattern of the excitonic order parameter. Our results imply that potentially interesting nonequilibrium physics is caused by rich local structural patterns involved in quasicrystals.We study the photoinduced dynamics of the excitonic insulator in the two-orbital Hubbard model on the Penrose tiling by means of the time-dependent real-space mean-field approximation. We show that, with a single-cycle electric-field pulse, the bulk (spatially averaged) excitonic order parameter decreases in the Bardeen-Cooper-Schrieffer (BCS) regime, while it increases in the Bose-Einstein condensate (BEC) regime. This behavior is in common with the excitonic insulator in the square lattice reported previously. To explore the dynamics peculiar to the Penrose tiling, we examine the coordination number dependence of observables and analyze the perpendicular space. In the BEC regime, characteristic oscillations of the electron number at each site are induced by the pulse, which are not observed in normal crystals with single coordination number. On the other hand, the dynamics in the BCS regime is characterized by drastic change in the spatial pattern of the excitonic order parameter. Our results imply that potentially interesting nonequilibrium physics is caused by rich local structural patterns involved in quasicrystals.

arXiv:2107.05304Physical review. B./Physical review. BMar 25, 20223 citations

Quasiperiodic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlattices

Martijn van Noort, Mason Alexander Porter, Y. Yi +1 more

arXiv:math/0405112Journal of Nonlinear ScienceNov 8, 200620 citations

Quantum size effect and two-step condensation of ideal Bose atoms in an optical hard-wall nanotube

Ze Cheng

We consider a quasi-one-dimensional (quasi-1D) system that is an optical hard-wall nanotube with axial harmonic potential. This quasi-1D system possesses a quasi-1D harmonic potential that consists of a 1D harmonic trap along the z axis and a two-dimensional box trap in the x-y plane. Within the framework of quantum statistical mechanics, we find that in a quasi-1D harmonic potential, the generalized Bose-Einstein condensation (GBEC) can be classified into the two types. The first type of GBEC (GBEC_{1}) corresponds to T_{m}<T_{c}. The second type of GBEC (GBEC_{2}) corresponds to T_{c}<T_{m}. Here, T_{c} is the critical temperature of the first-step condensation and T_{m} is the critical temperature of the second-step condensation. There is a competitive mechanism between normal Bose-Einstein condensation (NBEC) and GBEC. We shall show that the standard transition temperature T_{c} is much larger than the transition temperature T_{n} of NBEC. Therefore, the state of NBEC does not occur in a quasi-1D harmonic potential. We have proposed an analytical solution to the problem of GBEC of ideal atoms in the quasi-1D harmonic potential. The number of noncondensed atoms in the first-step condensation is characterized by a series of elliptic theta functions and the number of noncondensed atoms in the second-step condensation is characterized by a single q-digamma function. If r denotes the tube radius, then this quasi-1D system can show the quantum size effect. There is a critical tube radius r_{c}. (1) If r>r_{c}, then the mediate condensate fraction N_{m}/N=0; (2) if r>r_{c}, then the standard transition temperature T_{c}=0; (3) if r>r_{c}, then T_{m}>T_{c} and this is the state of GBEC_{2}. The results of numerical calculation of the analytical solution predict many new experimental phenomena in the GBEC of ideal atoms in the quasi-1D harmonic potential. In the thermodynamic limit, the analytical expressions of the three critical temperatures and the three condensate fractions are derived.We consider a quasi-one-dimensional (quasi-1D) system that is an optical hard-wall nanotube with axial harmonic potential. This quasi-1D system possesses a quasi-1D harmonic potential that consists of a 1D harmonic trap along the z axis and a two-dimensional box trap in the x-y plane. Within the framework of quantum statistical mechanics, we find that in a quasi-1D harmonic potential, the generalized Bose-Einstein condensation (GBEC) can be classified into the two types. The first type of GBEC (GBEC_{1}) corresponds to T_{m}<T_{c}. The second type of GBEC (GBEC_{2}) corresponds to T_{c}<T_{m}. Here, T_{c} is the critical temperature of the first-step condensation and T_{m} is the critical temperature of the second-step condensation. There is a competitive mechanism between normal Bose-Einstein condensation (NBEC) and GBEC. We shall show that the standard transition temperature T_{c} is much larger than the transition temperature T_{n} of NBEC. Therefore, the state of NBEC does not occur in a quasi-1D harmonic potential. We have proposed an analytical solution to the problem of GBEC of ideal atoms in the quasi-1D harmonic potential. The number of noncondensed atoms in the first-step condensation is characterized by a series of elliptic theta functions and the number of noncondensed atoms in the second-step condensation is characterized by a single q-digamma function. If r denotes the tube radius, then this quasi-1D system can show the quantum size effect. There is a critical tube radius r_{c}. (1) If r>r_{c}, then the mediate condensate fraction N_{m}/N=0; (2) if r>r_{c}, then the standard transition temperature T_{c}=0; (3) if r>r_{c}, then T_{m}>T_{c} and this is the state of GBEC_{2}. The results of numerical calculation of the analytical solution predict many new experimental phenomena in the GBEC of ideal atoms in the quasi-1D harmonic potential. In the thermodynamic limit, the analytical expressions of the three critical temperatures and the three condensate fractions are derived.

Physical review. EMay 13, 20260 citations

Bose-Einstein condensation of magnons in magnets with predominant ferromagnetic interactions

A. V. Syromyatnikov

We discuss Bose-Einstein condensation (BEC) of magnons in magnets with predominant ferromagnetic (FM) interaction in a magnetic field $H$ near saturation $({H}_{c})$ . Because ${H}_{c}$ is independent of FM couplings, magnetic materials of this type can have small ${H}_{c}$ which makes them promising candidates for experimental investigation of BECs. Ferromagnets with easy-plane anisotropy and antiferromagnets (AFs) containing weakly coupled FM planes or chains are discussed in detail. We observe a small effective interaction between magnons near the quantum critical point in such magnets, in contrast to the AFs with strong AF coupling previously discussed. In particular, this smallness allows us to find crossovers in the critical temperature ${T}_{c}(H)\ensuremath{\propto}{({H}_{c}\ensuremath{-}H)}^{1∕\ensuremath{\phi}}$ from $\ensuremath{\phi}=3∕2$ to $\ensuremath{\phi}=1$ in quasi-one-dimensional magnets, and from $\ensuremath{\phi}=3∕2$ to $\ensuremath{\phi}\ensuremath{\approx}1$ $({T}_{c}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}{T}_{c}\ensuremath{\propto}{H}_{c}\ensuremath{-}H)$ in quasi-two-dimensional ones.We discuss Bose-Einstein condensation (BEC) of magnons in magnets with predominant ferromagnetic (FM) interaction in a magnetic field $H$ near saturation $({H}_{c})$. Because ${H}_{c}$ is independent of FM couplings, magnetic materials of this type can have small ${H}_{c}$ which makes them promising candidates for experimental investigation of BECs. Ferromagnets with easy-plane anisotropy and antiferromagnets (AFs) containing weakly coupled FM planes or chains are discussed in detail. We observe a small effective interaction between magnons near the quantum critical point in such magnets, in contrast to the AFs with strong AF coupling previously discussed. In particular, this smallness allows us to find crossovers in the critical temperature ${T}_{c}(H)\ensuremath{\propto}{({H}_{c}\ensuremath{-}H)}^{1∕\ensuremath{\phi}}$ from $\ensuremath{\phi}=3∕2$ to $\ensuremath{\phi}=1$ in quasi-one-dimensional magnets, and from $\ensuremath{\phi}=3∕2$ to $\ensuremath{\phi}\ensuremath{\approx}1$ $({T}_{c}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}{T}_{c}\ensuremath{\propto}{H}_{c}\ensuremath{-}H)$ in quasi-two-dimensional ones.

arXiv:cond-mat/0610536Physical Review BApr 25, 200722 citations

Vortex Chain Structure in Bose-Einstein Condensates(General)

Tomoya Isoshima

Journal of the Physical Society of JapanSep 15, 20080 citations

We discuss Bose-Einstein condensation (BEC) of magnons in magnets with predominant ferromagnetic (FM) interaction in a magnetic field

H

near saturation

({H}_{c})

. Because

{H}_{c}

is independent of FM couplings, magnetic materials of this type can have small

{H}_{c}

which makes them promising candidates for experimental investigation of BECs. Ferromagnets with easy-plane anisotropy and antiferromagnets (AFs) containing weakly coupled FM planes or chains are discussed in detail. We observe a small effective interaction between magnons near the quantum critical point in such magnets, in contrast to the AFs with strong AF coupling previously discussed. In particular, this smallness allows us to find crossovers in the critical temperature ${T}_{c}(H)\ensuremath{\propto}{({H}_{c}\ensuremath{-}H)}^{1∕\ensuremath{\phi}}$ from $\ensuremath{\phi}=3∕2$ to $\ensuremath{\phi}=1$ in quasi-one-dimensional magnets, and from $\ensuremath{\phi}=3∕2$ to $\ensuremath{\phi}\ensuremath{\approx}1$ $({T}_{c}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}{T}_{c}\ensuremath{\propto}{H}_{c}\ensuremath{-}H)$ in quasi-two-dimensional ones.