Browsing by Author "Yang, Li"
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Item Bose-Fermi mapping and a multibranch spin-chain model for strongly interacting quantum gases in one dimension: Dynamics and collective excitations(American Physical Society, 2016) Yang, Li; Pu, Han; Rice Center for Quantum MaterialsWe show that the wave function in one spatial sector x1Item Dynamic Pricing Strategies(2021-04-29) Yang, Li; Pazgal, AmitPricing has been an intense research problem for a long time and my thesis mainly focuses on the pricing problem in the scenario where consumers often don’t know their exact valuations about the product before their purchase. After purchasing and using the product, they know their true valuations and then decide whether to keep the product or return it back to the seller with a refund. My dissertation work is mainly focused on how the sellers make use of such match uncertainty to orchestrate and design the optimal price prices and refund policies for different consumer segments in the market.Item Unknown One-body density matrix and momentum distribution of strongly interacting one-dimensional spinor quantum gases(American Physical Society, 2017) Yang, Li; Pu, HanThe one-body density matrix (OBDM) and the momentum distribution of quantum many-body systems are usually very difficult to calculate. Here we develop a technique to calculate the OBDM and the momentum distribution of a general one-dimensional (1D) spinor quantum gas in the strong interaction regime. This technique relies on a remarkable connection between the OBDM of the spinor gas and that of a spinless 1D hard-core anyon gas, which allows us to efficiently calculate the OBDM of the spinor system with particle numbers much larger than what was previously possible. Given the OBDM, we can easily calculate the momentum distribution of the spinor system, which is also related to the momentum distribution of the hard-core anyon gas. Our study not only provides a practical method for the calculation of the OBDM, but also provides significant insights into the properties of 1D strongly interacting spinor quantum gases.Item Unknown Strongly Interacting One-Dimensional Spinor Quantum Gases(2019-02-05) Yang, Li; Pu, HanQuantum many-body physics has been studied for many decades. A lot of intriguing phenomena have been observed and theories have been developed. Yet many problems remain unsolved, which is largely due to a lack of general efficient classical computation method. One-dimensional (1D) systems have also drawn much attention over the past few decades. One reason is that many unique strongly correlated quantum phenomena only appear in low dimensions. Another reason is that many exact results can be obtained in 1D for cross benchmarking, such as Bethe Ansatz, Bosonization, Bose-Fermi mapping, etc. In addition, many numerical methods, such as Matrix-Product-State based and Monte Carlo methods, work most efficiently in 1D. In recent years, 1D quantum gases have been realized in many cold atom labs, providing experimental motivation for their studies. One of the most mysterious assumptions about a system of identical quantum particles is that the wavefunction must be symmetric (for bosons) or anti-symmetric (for fermions). This means that no two fermions can occupy the same state, while multiple occupancy is allowed for bosons. Bosons and fermions are therefore generally very different. But in 1D this distinction could become rather subtle, provided that the bosonic multiple occupancy is suppressed, which can happen if strong repulsion exists between them. However, when considering spin degrees of freedom, things become more complicated. In this work, we develop a generalized Bose-Fermi mapping theory, under which, the charge degrees of freedom is mapped to a spinless fermions, while the spin degrees of freedom to an effective spin chain. This mapping works for arbitrary spin, arbitrary trapping potentials, arbitrary spin-dependent interaction potential, and for either spinor bosons or fermions. In the strong interaction limit, the wavefunction of the system is represented by the strong coupling ansatz wavefunction (SCAW), which takes the form of a direct product of spinless fermions wavefunction and spin wavefunction. Using this mapping technique, we study the dynamics and collective modes of the system. Furthermore, we develop a very efficient method to calculate the one-body density matrix, from which we can calculate the momentum distribution of the system.Item Unknown Strongly interacting quantum gases in one-dimensional traps(American Physical Society, 2015) Yang, Li; Guan, Liming; Pu, Han; Rice Quantum InstituteUnder second-order degenerate perturbation theory, we show that the physics of N particles with arbitrary spin confined in a one-dimensional trap in the strongly interacting regime can be described by superexchange interaction. An effective spin-chain Hamiltonian (non-translationally-invariant Sutherland model) can be constructed from this procedure. For spin-1/2 particles, this model reduces to the non-translationally-invariant Heisenberg model, where a transition between Heisenberg antiferromagnetic (AFM) and ferromagnetic (FM) states is expected to occur when the interaction strength is tuned from the strongly repulsive to the strongly attractive limit. We show that the FM and the AFM states can be distinguished by two different methods: the first is based on their distinct responses to a spin-dependent magnetic gradient, and the second is based on their distinct momentum distributions. We confirm the validity of the spin-chain model by comparison with results obtained from several unbiased techniques.