Ab initio based investigation of thermal transport in superlattices using the Boltzmann equation: Assessing the role of phonon coherence

The role of the coherent interference of phonons on thermal transport in artificial materials such as superlattices is of intense interest. Recent experimental studies report a non-monotonic trend in thermal conductivity with interface density which is attributed to band-folding of thermal phonons. Various models have been proposed to interpret these measurements, but most make simplifying assumptions that make definitively attributing the trends to the coherent transport difficult. Here, we investigate thermal transport in superlattices in the incoherent limit using the Boltzmann equation with intrinsic phonon dispersions and lifetimes calculated from first-principles. We find that the Boltzmann equation is unable to predict the non-monotonic behavior of thermal conductivity versus superlattice period, supporting the interpretation of phonon interference in recent experiments

Ab initio based investigation of thermal transport in superlattices using the Boltzmann equation: Assessing the role of phonon coherence

The role of the coherent interference of phonons on thermal transport in artificial materials such as superlattices is of intense interest. Recent experimental studies report a non-monotonic trend in thermal conductivity with interface density which is attributed to band-folding of thermal phonons. Various models have been proposed to interpret these measurements, but most make simplifying assumptions that make definitively attributing the trends to the coherent transport difficult. Here, we investigate thermal transport in superlattices in the incoherent limit using the Boltzmann equation with intrinsic phonon dispersions and lifetimes calculated from first-principles. We find that the Boltzmann equation is unable to predict the non-monotonic behavior of thermal conductivity versus superlattice period, supporting the interpretation of phonon interference in recent experiments

Reducing Computational Costs for Many-Body Physics Problems

Three different computational physics problems are discussed. The first project is solving the semi-classical Boltzmann transport equation (BTE) to compute the thermal conductivity of 1-D superlattices. We consider various spectral scattering models at each interface. This computation requires the inversion of a matrix whose size scales with the number of points used in the discretization of the Brillouin zone. We use spatial symmetries to reduce the size of data points and make the computation manageable. The other two projects involve quantum systems. Simulating quantum systems can potentially require exponential resources because of the exponential scaling of Hilbert space with system size. However, it has been observed that many physical systems, which typically exhibit locality in space or time, require much fewer resources to accurately simulate within some small error tolerance. The second project in the thesis is a two-step factorization of the electronic structure Hamiltonian that allows for efficient implementation on a quantum computer and also systematic truncation of small contributions. By using truncations that only incur errors below chemical accuracy, one is able to reduce the number of terms in the Hamiltonian from O(N⁴) to O(N³), where N is the number of molecular orbitals in the system. The third project is a tensor network algorithm based on the concept of influence functionals (IFs) to compute long-time dynamics of single-site observables. IFs are high-dimensional objects that describe the influence of the bath on the dynamics of the subsystem of interest over all times, and we are interested in their low-rank approximations. We study two numerical models, the spin-boson model and a model of interacting hard-core bosons in a 1D harmonic trap, and find that the IFs can be efficiently computed and represented using tensor network methods. Consistent with physical intuition, the correlations in the IFs appear to decrease with increased bath sizes, suggesting that the low-rank nature of the IF is due to nontrivial cancellations in the bath.</p

Low rank representations for quantum simulation of electronic structure

The quantum simulation of quantum chemistry is a promising application of quantum computers. However, for N molecular orbitals, the $\mathcal{O}(N^4)$ gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes simulation based on such primitives challenging. We substantially reduce the gate complexity of such primitives through a two-step low-rank factorization of the Hamiltonian and cluster operator, accompanied by truncation of small terms. Using truncations that incur errors below chemical accuracy, we are able to perform Trotter steps of the arbitrary basis electronic structure Hamiltonian with $\mathcal{O}(N^3)$ gate complexity in small simulations, which reduces to $\mathcal{O}(N^2 \log N)$ gate complexity in the asymptotic regime, while our unitary Coupled Cluster Trotter step has $\mathcal{O}(N^3)$ gate complexity as a function of increasing basis size for a given molecule. In the case of the Hamiltonian Trotter step, these circuits have $\mathcal{O}(N^2)$ depth on a linearly connected array, an improvement over the $\mathcal{O}(N^3)$ scaling assuming no truncation. As a practical example, we show that a chemically accurate Hamiltonian Trotter step for a 50 qubit molecular simulation can be carried out in the molecular orbital basis with as few as 4,000 layers of parallel nearest-neighbor two-qubit gates, consisting of fewer than 100,000 non-Clifford rotations. We also apply our algorithm to iron-sulfur clusters relevant for elucidating the mode of action of metalloenzymes.Comment: 8 pages, 4 figure

Mapping of recent brachiopod microstructure: a tool for environmental studies

Shells of brachiopods are excellent archives for environmental reconstructions in the recent and distant past as their microstructure and geochemistry respond to climate and environmental forcings. We studied the morphology and size of the basic structural unit, the secondary layer fibre, of the shells of several extant brachiopod taxa to derive a model correlating microstructural patterns to environmental conditions. Twenty-one adult specimens of six recent brachiopod species adapted to different environmental conditions, from Antarctica, to New Zealand, to the Mediterranean Sea, were chosen for microstructural analysis using SEM, TEM and EBSD. We conclude that: 1) there is no significant difference in the shape and size of the fibres between ventral and dorsal valves, 2) there is an ontogenetic trend in the shape and size of the fibres, as they become larger, wider, and flatter with increasing age. This indicates that the fibrous layer produced in the later stages of growth, which is recommended by the literature to be the best material for geochemical analyses, has a different morphostructure and probably a lower organic content than that produced earlier in life.&nbsp; In two species of the same genus living in seawater with different temperature and carbonate saturation state, a relationship emerged between the microstructure and environmental conditions. Fibres of the polar L. uva tend to be smaller, rounder and less convex than those of the temperate L. neozelanica, suggesting a relationship between microstructural size, shell organic matter content, ambient seawater temperature and calcite saturation state

Selective Ablation of Cancer Cells with Low Intensity Pulsed Ultrasound

Ultrasound can be focused into deep tissues with millimeter precision to perform noninvasive ablative therapy for diseases such as cancer. In most cases, this ablation uses high intensity ultrasound to deposit nonselective thermal or mechanical energy at the ultrasound focus, damaging both healthy bystander tissue and cancer cells. Here, we describe an alternative low intensity (I_(SPTA) 20 ms causes selective disruption of a panel of breast, colon, and leukemia cancer cell models in suspension without significantly damaging healthy immune or red blood cells. Mechanistic experiments reveal that the formation of acoustic standing waves and the emergence of cell-seeded cavitation lead to cytoskeletal disruption, expression of apoptotic markers, and cell death. The inherent selectivity of this low intensity pulsed ultrasound approach offers a potentially safer and thus more broadly applicable alternative to nonselective high intensity ultrasound ablation

Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution

The accurate computation of Hamiltonian ground, excited and thermal states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to machine learning. Given the challenges posed in constructing large-scale quantum computers, these tasks should be carried out in a resource-efficient way. In this regard, existing techniques based on phase estimation or variational algorithms display potential disadvantages; phase estimation requires deep circuits with ancillae, that are hard to execute reliably without error correction, while variational algorithms, while flexible with respect to circuit depth, entail additional high-dimensional classical optimization. Here, we introduce the quantum imaginary time evolution and quantum Lanczos algorithms, which are analogues of classical algorithms for finding ground and excited states. Compared with their classical counterparts, they require exponentially less space and time per iteration, and can be implemented without deep circuits and ancillae, or high-dimensional optimization. We furthermore discuss quantum imaginary time evolution as a subroutine to generate Gibbs averages through an analogue of minimally entangled typical thermal states. Finally, we demonstrate the potential of these algorithms via an implementation using exact classical emulation as well as through prototype circuits on the Rigetti quantum virtual machine and Aspen-1 quantum processing unit

Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution

The accurate computation of Hamiltonian ground, excited, and thermal states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to machine learning. Given the challenges posed in constructing large-scale quantum computers, these tasks should be carried out in a resource-efficient way. In this regard, existing techniques based on phase estimation or variational algorithms display potential disadvantages; phase estimation requires deep circuits with ancillae, that are hard to execute reliably without error correction, while variational algorithms, while flexible with respect to circuit depth, entail additional high-dimensional classical optimization. Here, we introduce the quantum imaginary time evolution and quantum Lanczos algorithms, which are analogues of classical algorithms for finding ground and excited states. Compared to their classical counterparts, they require exponentially less space and time per iteration, and can be implemented without deep circuits and ancillae, or high-dimensional optimization. We furthermore discuss quantum imaginary time evolution as a subroutine to generate Gibbs averages through an analog of minimally entangled typical thermal states. Finally, we demonstrate the potential of these algorithms via an implementation using exact classical emulation as well as through prototype circuits on the Rigetti quantum virtual machine and Aspen-1 quantum processing unit.Comment: 18 pages, 7 figures; improved figures and tex