scholarly journals Topological holographic quench dynamics in a synthetic frequency dimension

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Danying Yu ◽  
Bo Peng ◽  
Xianfeng Chen ◽  
Xiong-Jun Liu ◽  
Luqi Yuan
Keyword(s):  
Quantum Dynamics ◽  
Dimensional Space ◽  
Dynamical Evolution ◽  
Spin Model ◽  
Ring Resonators ◽  
Nonequilibrium Dynamics ◽  
Topological Phases ◽  
Time Dimension ◽  
Efficient Scheme ◽  
Quench Dynamics

AbstractThe notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of nonequilibrium topological invariants is a central issue and usually necessitates the information of quantum dynamics in both the time and momentum dimensions. Here, we propose the topological holographic quench dynamics in synthetic dimension, and also show it provides a highly efficient scheme to characterize photonic topological phases. A pseudospin model is constructed with ring resonators in a synthetic lattice formed by frequencies of light, and the quench dynamics is induced by initializing a trivial state, which evolves under a topological Hamiltonian. Our key prediction is that the complete topological information of the Hamiltonian is encoded in quench dynamics solely in the time dimension, and is further mapped to lower-dimensional space, manifesting the holographic features of the dynamics. In particular, two fundamental time scales emerge in the dynamical evolution, with one mimicking the topological band on the momentum dimension and the other characterizing the residue time evolution of the state after the quench. For this, a universal duality between the quench dynamics and the equilibrium topological phase of the spin model is obtained in the time dimension by extracting information from the field evolution dynamics in modulated ring systems in simulations. This work also shows that the photonic synthetic frequency dimension provides an efficient and powerful way to explore the topological nonequilibrium dynamics.

scholarly journals Magnetic properties and quench dynamics of two interacting ultracold molecules in a trap

2020 ◽  
Vol 22 (48) ◽  
pp. 28140-28153
Author(s):  
Anna Dawid ◽  
Michał Tomza
Keyword(s):  
Magnetic Properties ◽  
Internal Structure ◽  
Nonequilibrium Dynamics ◽  
External Fields ◽  
Ultracold Molecules ◽  
Quench Dynamics

The interplay of external fields and internal structure of two interacting ultracold trapped molecules produces rich magnetization diagrams and nonequilibrium dynamics.

Spinning strings of the Neveu-Schwarz-Ramond type in 3, 4, 6, and 10 space-time dimensions

1999 ◽  
Vol 77 (6) ◽  
pp. 427-446
Author(s):  
S B Phillips
Keyword(s):  
Degrees Of Freedom ◽  
Lagrangian Density ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Physical Space ◽  
Space Time ◽  
Coordinate Space ◽  
Time Dimension ◽  
Light Cone Gauge ◽  
Fermionic Sector

A model of a spinning string with an internal coordinate index is proposed and studied. When the action for this model is taken to be diagonal in this internal coordinate space and quantized in the light-cone gauge it is found to be Lorentz covariant in four-dimensional space-time provided that the internal coordinate space is four dimensional.This combination of space-time dimension, D, and internal coordinate space dimension, N, is just one of four possible sets, the other three corresponding to D = 3, 6, and 10, precisely the same values for which it is possible to formulate Yang-Mills theories with simple supersymmetry. By comparing the number of propagating degrees of freedom at the zero-mass level in the open string bosonic and fermionic sectors it is found that a supersymmetric interpretation of this model is possible provided that all physical states in the bosonic sector have even G-parity and the ground-state spin or in the fermionic sector have positive chirality. A possible interpretation of the connection betweenthe N components of each of the D space-time coordinates is presentedon the basis that the space-time coordinates are scalars in the internal coordinate space. This interpretation would appear to be reasonable given the fact that the field variables in the Lagrangian density do not necessarily have to represent physically measurable quantities but can, instead, only represent physically measurable quantities when combined in some manner, the simplest of which being a linear combination. The Lagrangian density simply produces the equations of motion and the constraint equations for the independent variables, only linear combinations of which represent the four dimensions of physical space-time.PACS Nos.: 11.17.+y, 11.10.Qr, 1.30.Cp, 11.30.Pb

scholarly journals THE LOW ENERGY EFFECTIVE LAGRANGIAN FOR PHOTON INTERACTIONS IN ANY DIMENSION

1996 ◽  
Vol 11 (02) ◽  
pp. 253-269 ◽  
Author(s):  
A. RITZ ◽  
R. DELBOURGO
Keyword(s):  
Dimensional Space ◽  
Effective Interaction ◽  
Bernoulli Polynomial ◽  
Weak Field ◽  
Space Time ◽  
Low Energy ◽  
Time Dimension ◽  
Effective Lagrangian ◽  
Dimensional Space Time ◽  
Photon Interactions

The subject of low energy photon-photon scattering is considered in arbitrary-dimensional space-time and the interaction is widened to include scattering events involving an arbitrary number of photons. The effective interaction Lagrangian for these processes in QED has been determined in a manifestly invariant form. This generalization resolves the structure of the weak field Euler-Heisenberg Lagrangian and indicates that the component invariant functions have coefficients related not only to the space-time dimension but also to the coefficients of the Bernoulli polynomial.

scholarly journals Topological phases, Majorana modes and quench dynamics in a spin ladder system

2011 ◽  
Vol 13 (6) ◽  
pp. 065028 ◽  
Author(s):  
Wade DeGottardi ◽  
Diptiman Sen ◽  
Smitha Vishveshwara
Keyword(s):  
Spin Ladder ◽  
Topological Phases ◽  
Ladder System ◽  
Majorana Modes ◽  
Quench Dynamics

scholarly journals Layer-Based Data Aggregation and Performance Analysis in Wireless Sensor Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hongju Cheng ◽  
Yongzhao Chen ◽  
Naixue Xiong ◽  
Feifei Li
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Data Aggregation ◽  
Dimensional Space ◽  
Scheduling Algorithm ◽  
Wireless Sensor ◽  
Efficient Scheme ◽  
Aggregation Tree ◽  
Practical Performance ◽  
And Performance

Due to the similarity and correlation among sensed data in wireless sensor network, it is an important way to reduce the number of packets transmitted with data aggregation technology so as to prolong the network lifetime. However, data aggregation is still a challenging issue since quality-of-service, such as end-to-end delay, is generally considered as a severe criterion required in many applications. We focus on the minimum-latency data aggregation problem and proposed a new efficient scheme for it. The basic idea is that we first build an aggregation tree by ordering nodes into layers, and then we proposed a scheduling algorithm on the basis of the aggregation tree to determine the transmission time slots for all nodes in the network with collision avoiding. We have proved that the upper bound for data aggregation with our proposed scheme is bounded by(15R+Δ-15)for wireless sensor networks in two-dimensional space. Extensive simulation results have demonstrated that the proposed scheme has better practical performance compared with related works.

scholarly journals Rotational Flocking with Spontaneous Directional Changes

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Xiaolu Liu ◽  
Guanbo Shao ◽  
Yudong Tang ◽  
Duxin Chen
Keyword(s):  
Decision Making ◽  
Dynamical Evolution ◽  
Transient State ◽  
Spin Model ◽  
Theoretical Derivation ◽  
Individual Preferences ◽  
Distinct Individual ◽  
Energy Equilibrium ◽  
Behavioral Transition ◽  
Rotational Direction

Revealing the underlying decision-making strategy governing the high-group polarization accompanied by conflicting individual preferences may play a central part in the lives of social animals. Hereby, we construct a structured spin model in accordance with empirical validation, which shows how distinct individual preferences converge from one consensus homeostasis to another lowest-energy equilibrium. To verify the theoretical derivation, we use high-resolution spatiotemporal GPS data of a flock of thirty pigeons and study the dynamical evolution mechanism of systemic spins. Therein, we find successful rotational direction transitions requiring a sufficient number of supporters. A few initiators trigger the phase transition from one equilibrium to another, where the symmetric transient state indicates a diamond hierarchical network being completed by the intermediates and the rear individuals. By further studying the nature, we reveal that decision-making sequences are strongly triggered and influenced by individual positions and the leader-follower relationship. Thus, we can predict which individual is more likely to make the decision before the initial transition moment and who will draw the complete stop. Consequently, the revealed decision-making strategy facilitates a comprehensive understanding of collective behavioral transition.

Molecular nanomagnets

2017 ◽  
Author(s):  
W. Wernsdorfer
Keyword(s):  
Molecular Electronics ◽  
Single Molecule ◽  
Quantum Dynamics ◽  
Spin Model ◽  
Photon Absorption ◽  
Single Molecule Magnets ◽  
Molecular Nanomagnets ◽  
Quantum Properties ◽  
Molecular Spintronics ◽  
Quantum Phenomena

This article describes the quantum phenomena observed in molecular nanomagnets. Molecular nanomagnets, or single-molecule magnets (SMMs), provides a fundamental link between spintronics and molecular electronics. SMMs combine the classic macroscale properties of a magnet with the quantum properties of a nanoscale entity. The resulting field, molecular spintronics, aims at manipulating spins and charges in electronic devices containing one or more molecules. This article first considers molecular nanomagnets and the giant spin model for nanomagnets before discussing the quantum dynamics of a dimer of nanomagnets, resonant photon absorption in Cr7Ni antiferromagnetic rings, and photon-assisted tunnelling in a single-molecule magnet. It also examines environmental decoherence effects in nanomagnets and concludes by highlighting the new trends towards molecular spintronics using junctions and nano-SQUIDs.

scholarly journals Many-body topological invariants from randomized measurements in synthetic quantum matter

2020 ◽  
Vol 6 (15) ◽  
pp. eaaz3666 ◽  
Author(s):  
Andreas Elben ◽  
Jinlong Yu ◽  
Guanyu Zhu ◽  
Mohammad Hafezi ◽  
Frank Pollmann ◽  
...  
Keyword(s):  
Body Wave ◽  
Complete Classification ◽  
Theoretical Description ◽  
Spin Model ◽  
Topological Invariants ◽  
Topological Phases ◽  
Many Body ◽  
Topological Quantum ◽  
The Many ◽  
Symmetry Protected

Many-body topological invariants, as quantized highly nonlocal correlators of the many-body wave function, are at the heart of the theoretical description of many-body topological quantum phases, including symmetry-protected and symmetry-enriched topological phases. Here, we propose and analyze a universal toolbox of measurement protocols to reveal many-body topological invariants of phases with global symmetries, which can be implemented in state-of-the-art experiments with synthetic quantum systems, such as Rydberg atoms, trapped ions, and superconducting circuits. The protocol is based on extracting the many-body topological invariants from statistical correlations of randomized measurements, implemented with local random unitary operations followed by site-resolved projective measurements. We illustrate the technique and its application in the context of the complete classification of bosonic symmetry-protected topological phases in one dimension, considering in particular the extended Su-Schrieffer-Heeger spin model, as realized with Rydberg tweezer arrays.

scholarly journals Thermal inclusions: how one spin can destroy a many-body localized phase

2017 ◽  
Vol 375 (2108) ◽  
pp. 20160428 ◽  
Author(s):  
Pedro Ponte ◽  
C. R. Laumann ◽  
David A. Huse ◽  
A. Chandran
Keyword(s):  
Random Fields ◽  
Quantum Dynamics ◽  
Quantum Systems ◽  
Spin Model ◽  
Single Site ◽  
Level System ◽  
Many Body ◽  
Discontinuous Transition ◽  
Logarithmic Corrections ◽  
Basic Features

Many-body localized (MBL) systems lie outside the framework of statistical mechanics, as they fail to equilibrate under their own quantum dynamics. Even basic features of MBL systems, such as their stability to thermal inclusions and the nature of the dynamical transition to thermalizing behaviour, remain poorly understood. We study a simple central spin model to address these questions: a two-level system interacting with strength J with N ≫1 localized bits subject to random fields. On increasing J , the system transitions from an MBL to a delocalized phase on the vanishing scale J c ( N )∼1/ N , up to logarithmic corrections. In the transition region, the single-site eigenstate entanglement entropies exhibit bimodal distributions, so that localized bits are either ‘on’ (strongly entangled) or ‘off’ (weakly entangled) in eigenstates. The clusters of ‘on’ bits vary significantly between eigenstates of the same sample, which provides evidence for a heterogeneous discontinuous transition out of the localized phase in single-site observables. We obtain these results by perturbative mapping to bond percolation on the hypercube at small J and by numerical exact diagonalization of the full many-body system. Our results support the arguments that the MBL phase is unstable in systems with short-range interactions and quenched randomness in dimensions d that are high but finite. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.

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