arXiv subjects

Lei Tan

Publications and source records attributed to Lei Tan.

At least 73 records · Page 4Linked to original sources

arXiv2017

Auxiliary-cavity-assisted ground-state cooling of optically levitated nanosphere in the unresolved-sideband regime

We theoretically analyse the ground-state cooling of optically levitated nanosphere in unresolved- sideband regime by introducing a coupled high-quality-factor cavity. On account of the quantum interference stemming from the presence of the coupled cavity, the spectral density of the optical force exerting on the nanosphere gets changed and then the symmetry between the heating and the cooling processes is broken. Through adjusting the detuning of strong-dissipative cavity mode, one obtains an enhanced net cooling rate for the nanosphere. It is illustrated that the ground state cooling can be realized in the unresolved sideband regime even if the effective optomechanical coupling is weaker than the frequency of the nanosphere, which can be understood by the picture that the effective interplay of the nanosphere and the auxiliary cavity mode brings the system back to an effective resolved regime. Besides, the coupled cavity refines the dynamical stability of the system.

quant-ph↗

arXiv2017

Quantum phase transitions of light in a dissipative Dicke-Bose-Hubbard model

The impacts that the environment has on the quantum phase transition of light in the DickeBose-Hubbard model are investigated. Based on the quasibosonic approach, mean field theory and the perturbation theory, the formulation of the Hamiltonian, the eigenenergies and the superfluid order parameter are obtained analytically. Compared with the ideal cases, the order parameter of the system evolves with time as the photons naturally decay in their environment. When the system starts with the superfluid state, the dissipation makes the photons tend to localize, and a greater hopping energy of photon is required to restore the long-range phase coherence of the localized state of the system. Furthermore, the Mott lobes disappears and the system tends to be classical with the number of atoms increasing; however, the atomic number is far lower than that expected under ideal circumstances. Therefore, our theoretical results offer valuable insight into the quantum phase transition of a dissipative system.

quant-ph↗

arXiv2016

Panoptic Studio: A Massively Multiview System for Social Interaction Capture

We present an approach to capture the 3D motion of a group of people engaged in a social interaction. The core challenges in capturing social interactions are: (1) occlusion is functional and frequent; (2) subtle motion needs to be measured over a space large enough to host a social group; (3) human appearance and configuration variation is immense; and (4) attaching markers to the body may prime the nature of interactions. The Panoptic Studio is a system organized around the thesis that social interactions should be measured through the integration of perceptual analyses over a large variety of view points. We present a modularized system designed around this principle, consisting of integrated structural, hardware, and software innovations. The system takes, as input, 480 synchronized video streams of multiple people engaged in social activities, and produces, as output, the labeled time-varying 3D structure of anatomical landmarks on individuals in the space. Our algorithm is designed to fuse the "weak" perceptual processes in the large number of views by progressively generating skeletal proposals from low-level appearance cues, and a framework for temporal refinement is also presented by associating body parts to reconstructed dense 3D trajectory stream. Our system and method are the first in reconstructing full body motion of more than five people engaged in social interactions without using markers. We also empirically demonstrate the impact of the number of views in achieving this goal.

cs.CV↗

arXiv2016

Rational maps as Schwarzian primitives

We study necessary and sufficient conditions for a meromorphic quadratic differential with prescribed poles to be the Schwarzian derivative of a rational map. We give geometric interpretations of these conditions. We also study the pole-dependency of these Schwarzian derivatives. We show that, in the cubic case, the analytic dependency fails precisely when the poles are displaced at the vertices of a regular ideal tetrahedron of the hyperbolic 3-ball.

math.CV↗

arXiv2015

Renormalization and wandering continua of rational maps

Renormalizations can be considered as building blocks of complex dynamical systems. This phenomenon has been widely studied for iterations of polynomials of one complex variable. Concerning non-polynomial hyperbolic rational maps, a recent work of Cui-Tan shows that these maps can be decomposed into postcritically finite renormalization pieces. The main purpose of the present work is to perform the surgery one step deeper. Based on Thurston's idea of decompositions along multicurves, we introduce a key notion of Cantor multicurves (a stable multicurve generating infinitely many homotopic curves under pullback), and prove that any postcritically finite piece having a Cantor multicurve can be further decomposed into smaller postcritically finite renormalization pieces. As a byproduct, we establish the presence of separating wandering continua in the corresponding Julia sets. Contrary to the polynomial case, we exploit tools beyond the category of analytic and quasiconformal maps, such as Rees-Shishikura's semi-conjugacy for topological branched coverings that are Thurston-equivalent to rational maps.

math.DS↗

arXiv2015

Hyperbolic-parabolic deformations of rational maps

We develop a Thurston-like theory to characterize geometrically finite rational maps, then apply it to study pinching and plumbing deformations of rational maps. We show that in certain conditions the pinching path converges uniformly and the quasiconformal conjugacy converges uniformly to a semi-conjugacy from the original map to the limit. Conversely, every geometrically finite rational map with parabolic points is the landing point of a pinching path for any prescribed plumbing combinatorics.

math.DS↗

arXiv2015

Renormalizations and wandering Jordan curves of rational maps

We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of uncountably many Jordan curve components. Most of them are wandering. The other consists of components that are pullbacks of finitely many renormalizations, together with possibly uncountably many points. The quotient action on the decomposed pieces is encoded by a dendrite dynamical system. We also introduce a surgery procedure to produce post-critically finite rational maps with wandering Jordan curves and prescribed renormalizations.

math.DS↗

arXiv2015

Agent-based model with multi-level herding for complex financial systems

In complex financial systems, the sector structure and volatility clustering are respectively important features of the spatial and temporal correlations. However, the microscopic generation mechanism of the sector structure is not yet understood. Especially, how to produce these two features in one model remains challenging. We introduce a novel interaction mechanism, i.e., the multi-level herding, in constructing an agent-based model to investigate the sector structure combined with volatility clustering. According to the previous market performance, agents trade in groups, and their herding behavior comprises the herding at stock, sector and market levels. Further, we propose methods to determine the key model parameters from historical market data, rather than from statistical fitting of the results. From the simulation, we obtain the sector structure and volatility clustering, as well as the eigenvalue distribution of the cross-correlation matrix, for the New York and Hong Kong stock exchanges. These properties are in agreement with the empirical ones. Our results quantitatively reveal that the multi-level herding is the microscopic generation mechanism of the sector structure, and provide new insight into the spatio-temporal interactions in financial systems at the microscopic level.

q-fin.GN↗

arXiv2015

How volatilities nonlocal in time affect the price dynamics in complex financial systems

What is the dominating mechanism of the price dynamics in financial systems is of great interest to scientists. The problem whether and how volatilities affect the price movement draws much attention. Although many efforts have been made, it remains challenging. Physicists usually apply the concepts and methods in statistical physics, such as temporal correlation functions, to study financial dynamics. However, the usual volatility-return correlation function, which is local in time, typically fluctuates around zero. Here we construct dynamic observables nonlocal in time to explore the volatility-return correlation, based on the empirical data of hundreds of individual stocks and 25 stock market indices in different countries. Strikingly, the correlation is discovered to be non-zero, with an amplitude of a few percent and a duration of over two weeks. This result provides compelling evidence that past volatilities nonlocal in time affect future returns. Further, we introduce an agent-based model with a novel mechanism, that is, the asymmetric trading preference in volatile and stable markets, to understand the microscopic origin of the volatility-return correlation nonlocal in time.

q-fin.GN↗

arXiv2014

Quantum phase transition in an array of coupled dissipative cavities

The features of superfluid-Mott insulator phase transition in the array of dissipative nonlinear cavities are analyzed. We show analytically that the coupling to the bath can be reduced to renormalizing the eigenmodes of atom-cavity system. This gives rise to a localizing effect and drives the system into mixed states. For the superfluid state, a dynamical instability will lead to a sweeping to a localized state of photons. For the Mott state, a dissipation-induced fluctuation will suppress the restoring of long-range phase coherence driven by interaction.

quant-ph↗

arXiv2014

Kneading with weights

We generalise Milnor-Thurston's kneading theory to the setting of piecewise continuous and monotone interval maps with weights. We define a weighted kneading determinant ${\cal D}(t)$ and establish combinatorially two kneading identities, one with the cutting invariant and one with the dynamical zeta function. For the pressure $\log ρ_1$ of the weighted system, playing the role of entropy, we prove that ${\cal D}(t)$ is non-zero when $|t|<1/ρ_1$ and has a zero at $1/ρ_1$. Furthermore, our map is semi-conjugate to an analytic family $h_t, 0 < t < 1/ρ_1$ of Cantor PL maps converging to an interval PL map $h_{1/ρ_1}$ with equal pressure

math.DS↗

arXiv2014

Agent-based model with asymmetric trading and herding for complex financial systems

Background: For complex financial systems, the negative and positive return-volatility correlations, i.e., the so-called leverage and anti-leverage effects, are particularly important for the understanding of the price dynamics. However, the microscopic origination of the leverage and anti-leverage effects is still not understood, and how to produce these effects in agent-based modeling remains open. On the other hand, in constructing microscopic models, it is a promising conception to determine model parameters from empirical data rather than from statistical fitting of the results. Methods: To study the microscopic origination of the return-volatility correlation in financial systems, we take into account the individual and collective behaviors of investors in real markets, and construct an agent-based model. The agents are linked with each other and trade in groups, and particularly, two novel microscopic mechanisms, i.e., investors' asymmetric trading and herding in bull and bear markets, are introduced. Further, we propose effective methods to determine the key parameters in our model from historical market data. Results: With the model parameters determined for six representative stock-market indices in the world respectively, we obtain the corresponding leverage or anti-leverage effect from the simulation, and the effect is in agreement with the empirical one on amplitude and duration. At the same time, our model produces other features of the real markets, such as the fat-tail distribution of returns and the long-term correlation of volatilities. Conclusions: We reveal that for the leverage and anti-leverage effects, both the investors' asymmetric trading and herding are essential generation mechanisms. These two microscopic mechanisms and the methods for the determination of the key parameters can be applied to other complex systems with similar asymmetries.

q-fin.ST↗

arXiv2014

On Parameter Space of Complex Polynomial Vector Fields in the Complex Plane

The space of degree d single-variable monic and centered complex polynomial vector fields can be decomposed into loci in which the vector fields have the same topological structure. We analyze the geometric structure of these loci and describe some bifurcations, in particular, it is proved that new homoclinic separatrices can form under small perturbation. By an example, we show that this decomposition of parameter space by combinatorial data is not a cell decomposition. The appendix to this article, joint work with Tan Lei, shows that landing separatrices are stable under small perturbation of the vector field if the multiplicities of the equilibrium points are preserved.

math.DS↗

arXiv2012

Bose-Einstein Condensates in a Cavity-mediated Triple-well

We investigate the energy structures and the dynamics of a Bose-Einstein condensates (BEC) in a triple-well potential coupled a high finesse optical cavity within a mean field approach. Due to the intrinsic atom-cavity field nonlinearity, several interesting phenomena arise which are the focuses of this work. For the energy structure, the bistability appears in the energy levels due to this atoms-cavity field nonlinearity, and the same phenomena can be found in the intra-cavity photons number. With an increase of the pump-cavity detunings, the higher and lower energy levels show a loop structure due to this cavity-mediated effects. In the dynamical process, an extensive numerical simulation of localization of the BECs for atoms initially trapped in one-, two-, and three-wells are performed for the symmetric and asymmetric cases in detail. It is shown that the the transition from oscillation to the localization can be modified by the cavity-mediated potential, which will enlarge the regions of oscillation. With the increasing of the atomic interaction, the oscillation is blocked and the localization emerges. The condensates atoms can be trapped either in one-, two-, or in three wells eventually where they are initially uploaded for certain parameters. In particular, we find that the transition from the oscillation to the localization is accompanied with some irregular regime where tunneling dynamics is dominated by chaos for this cavity-mediated system.

cond-mat.quant-gas↗

arXiv2012

Effects of Dipole-Dipole Interaction on the Transmitted spectrum of Two-level Atoms trapped in an optical cavity

The transmission spectrum of two dipole-dipole coupled atoms interacting with a single-mode optical cavity in strong coupling regime is investigated theoretically for the lower and higher excitation cases, respectively. The dressed states containing the dipole-dipole interaction (DDI) are obtained by transforming the two-atom system into an effective single-atom one. We found that the DDI can enhance the effects resulting from the positive atom-cavity detunings but weaken them for the negative detunings cases for lower excitation, which can promote the spectrum exhibiting two asymmetric peaks and shift the heights and the positions of them. For the higher excitation cases, DDI can augment the atomic saturation and lead to the deforming of the spectrum. Furthermore, the large DDI can make the atom and the cavity decouple, making a singlet of the normal-mode spectrum.

quant-ph↗

arXiv2011

Quantum phase transitions for two coupled sites with dipole-coupled effective Jaynes-Cummings model

The nature of the ground states for a system composed of two coupled cavities with each containing a pair of dipole-coupled two-level atoms are studied over a wide range of detunings and dipole coupling strengths. The cases for three limits of exact resonance, large positive and negative detunings are discussed, and four types of the ground states are revealed. Then the phase diagrams of the ground state are plotted by choosing three different "order parameters". We find that the phase space, determined by the combinative action of detuning and the dipole coupling strength, is divided into four regions. This is different from the general Bose-Hubbard model and more richer physics are presented in the two-site coupled cavities system. That is, the insulator region may be polaritonic or atomic and the superfluid region may be polaritonic or photonic in nature.

quant-ph↗

arXiv2011

Combinatorial rigidity of multicritical maps

We combine the KSS nest constructed by Kozlovski, Shen and van Strien, and the analytic method proposed by Avila, Kahn, Lyubich and Shen to prove the combinatorial rigidity of multicritical maps.

math.DS↗

arXiv2011

Localized tendency for the superfluid and Mott insulator state in the array of dissipative cavities

The features of superfluid-Mott insulator phase transition in the array of dissipative cavities is analyzed. Employing a kind of quasi-boson and a mean-filed approach, we show analytically how dissipation and decoherence influence the critical behaviors and the time evolution of the system. We find that there is a localized tendency, which could lead to the break of superfluidity for a superfluid state and suppress the appearance of the long-range order form a Mott state. Eventually, a collection of mixture states localized on each site will arise.

quant-ph↗