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1. A reaction network approach to the convergence to equilibrium of quantum Boltzmann equations for Bose gases

   https://doi.org/10.1051/cocv/2021079  

   Craciun, Gheorghe; Tran, Minh-Binh (January 2021, ESAIM: Control, Optimisation and Calculus of Variations)

   Buttazzo, G.; Casas, E.; de Teresa, L.; Glowinski, R.; Leugering, G.; Trélat, E.; Zhang, X. (Ed.)

   When the temperature of a trapped Bose gas is below the Bose-Einstein transition temperature and above absolute zero, the gas is composed of two distinct components: the Bose-Einstein condensate and the cloud of thermal excitations. The dynamics of the excitations can be described by quantum Boltzmann models. We establish a connection between quantum Boltzmann models and chemical reaction networks. We prove that the discrete differential equations for these quantum Boltzmann models converge to an equilibrium point. Moreover, this point is unique for all initial conditions that satisfy the same conservation laws. In the proof, we then employ a toric dynamical system approach, similar to the one used to prove the global attractor conjecture, to study the convergence to equilibrium of quantum kinetic equations. 

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2. Quantum critical dynamics in a spinor Hubbard model quantum simulator

   https://doi.org/10.1038/s42005-021-00562-y  

   Austin, Jared O.; Chen, Zihe; Shaw, Zachary N.; Mahmud, Khan W.; Liu, Yingmei (March 2021, Communications Physics)

   Abstract Three-dimensional (3D) strongly correlated many-body systems, especially their dynamics across quantum phase transitions, are prohibitively difficult to be numerically simulated. We experimentally demonstrate that such complex many-body dynamics can be efficiently studied in a 3D spinor Bose–Hubbard model quantum simulator, consisting of antiferromagnetic spinor Bose–Einstein condensates confined in cubic optical lattices. We find dynamics and scaling effects beyond the scope of existing theories at superfluid–insulator quantum phase transitions, and highlight spin populations as a good observable to probe the quantum critical dynamics. Our data indicate that the scaling exponents are independent of the nature of the quantum phase transitions. We also conduct numerical simulations in lower dimensions using time-dependent Gutzwiller approximations, which qualitatively describe our observations. 

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3. Protocol for Nonlinear State Discrimination in Rotating Condensate

   https://doi.org/10.1002/qute.202300431  

   Geller, Michael_R (May 2024, Advanced Quantum Technologies)

   Abstract Nonlinear mean field dynamics enables quantum information processing operations that are impossible in linear one‐particle quantum mechanics. In this approach, a register of bosonic qubits (such as neutral atoms or polaritons) is initialized into a symmetric product state through condensation, then subsequently controlled by varying the qubit‐qubit interaction. An experimental implementation of quantum state discrimination, an important subroutine in quantum computation, with a toroidal Bose–Einstein condensate is proposed. The condensed bosons here are atoms, each in the same superposition of angular momenta 0 and , encoding a qubit. A nice feature of the protocol is that only a readout of individual quantized circulation states (not superpositions) is required. 

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4. Numerical solution of large scale Hartree–Fock–Bogoliubov equations

   https://doi.org/10.1051/m2an/2020074  

   Lin, Lin; Wu, Xiaojie (May 2021, ESAIM: Mathematical Modelling and Numerical Analysis)

   The Hartree–Fock–Bogoliubov (HFB) theory is the starting point for treating superconducting systems. However, the computational cost for solving large scale HFB equations can be much larger than that of the Hartree–Fock equations, particularly when the Hamiltonian matrix is sparse, and the number of electrons N is relatively small compared to the matrix size N b . We first provide a concise and relatively self-contained review of the HFB theory for general finite sized quantum systems, with special focus on the treatment of spin symmetries from a linear algebra perspective. We then demonstrate that the pole expansion and selected inversion (PEXSI) method can be particularly well suited for solving large scale HFB equations. For a Hubbard-type Hamiltonian, the cost of PEXSI is at most 𝒪( N b 2 ) for both gapped and gapless systems, which can be significantly faster than the standard cubic scaling diagonalization methods. We show that PEXSI can solve a two-dimensional Hubbard-Hofstadter model with N b up to 2.88 × 10 6 , and the wall clock time is less than 100 s using 17 280 CPU cores. This enables the simulation of physical systems under experimentally realizable magnetic fields, which cannot be otherwise simulated with smaller systems. 

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5. Theory of Quantum Super Impulses

   https://doi.org/10.1103/PRXQuantum.5.010322  

   Jarzynski, Christopher (February 2024, PRX Quantum)

   A quantum impulse is a brief but strong perturbation that produces a sudden change in a wave function ψ (x). We develop a theory of quantum impulses, distinguishing between ordinary and super impulses. An ordinary impulse paints a phase onto ψ, while a super impulse—the main focus of this paper—deforms the wave function under an invertible map, μ : x → x′. Borrowing tools from optimal-mass-transport theory and shortcuts to adiabaticity, we show how to design a super impulse that deforms a wave func- tion under a desired map μ and we illustrate our results using solvable examples. We point out a strong connection between quantum and classical super impulses, expressed in terms of the path-integral formu- lation of quantum mechanics. We briefly discuss hybrid impulses, in which ordinary and super impulses are applied simultaneously. While our central results are derived for evolution under the time-dependent Schrödinger equation, they apply equally well to the time-dependent Gross-Pitaevskii equation and thus may be relevant for the manipulation of Bose-Einstein condensates. 

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