Tien Nguyen Thi Kieu - Academia.edu (original) (raw)

Papers by Tien Nguyen Thi Kieu

Research paper thumbnail of Mathematical Computability Questions for some Classes of Linear and Non-Linear Differential Equations Originated from Hilbert's Tenth Problem

Computability and Complexity in Analysis, 2005

Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of intege... more Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into problems involving either a set of infinitely-coupled non-linear differential equations or a class of linear Schrodinger equations with some appropriate time- dependent Hamiltonians. We then raise the questions whether these two classes of differential equations are computable or not in some computation models of

Research paper thumbnail of A reformulation of Hilbert's tenth problem through quantum mechanics

Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2004

Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer ar... more Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into either a problem involving a set of infinitely coupled differential equations or a problem involving a Shrödinger propagator with some appropriate kernel. Either way, Mathematics and Physics could be combined for Hilbert's tenth problem and for the notion of effective computability.

Research paper thumbnail of Finite temperature correlations in the Bose-Hubbard model: application of the Gauge <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span> representation

Cornell University - arXiv, Feb 25, 2010

We study ultracold Bose gases in periodic potentials as described by the Bose-Hubbard model. In 1... more We study ultracold Bose gases in periodic potentials as described by the Bose-Hubbard model. In 1D and at finite temperature, we simulate ultracold Bose gases in imaginary time with the gauge P representation. We study various quantities including the Luttinger parameter K, which is important for locating the boundaries of the Mott insulator lobes, and find a simple relation for the kinetic energy part of the Bose-Hubbard Hamiltonian. We show that for J = 0, the stepwise pattern of the average number of particles per lattice site versus the chemical potential vanishes at temperatures above T ≈ 0.1U. Also, at chemical potential µ = 0.5U and temperature T = 0.5U by increasing J, the relative value of the number fluctuation decreases and approaches that of a coherent state.

Research paper thumbnail of Quantum Central Limit Theorems, Emergence of Classicality and Time-dependent Differential Entropy

We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-gr... more We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators. Thanks to the hermicity constraints, we obtain positive-definite distribution for the expectation values of observables. These probability distributions open some pathway for an emergence of classical behaviours in the limit of infinitely large number of identical and non-interacting quantum constituents. This is in contradistinction to other mechanisms of classicality emergence due to environmental decoherence and consistent histories. The probability distributions so derived also enable us to evaluate the nontrivial time-dependence of certain differential entropies.

Research paper thumbnail of A numerical attempt on the chiral Schwinger model

Nuclear Physics B - Proceedings Supplements, 1995

The chiral Schwinger model is formulated in the wilson-fermion formulation on the lattice and the... more The chiral Schwinger model is formulated in the wilson-fermion formulation on the lattice and then simulated by the complex langevin algorithm. The simulation is done both without and with gauge xing to the Lorentz gauge for the compact gauge links. Some preliminary results are presented which indicate that the complex langevin is well behaving with the complex chiral fermion determinant.

Research paper thumbnail of Padé-Z2 stochastic estimator of determinants applied to quark loop expansion of lattice QCD

Nuclear Physics B - Proceedings Supplements, 2001

Research paper thumbnail of What's Wrong with Anomalous Chiral Gauge Theory?

Chinese Journal of Physics- Taipei-

It is argued on general ground and demonstrated in the particular example of the Chiral Schwinger... more It is argued on general ground and demonstrated in the particular example of the Chiral Schwinger Model that there is nothing wrong with apparently anomalous chiral gauge theory. If quantised correctly, there should be no gauge anomaly and chiral gauge theory should be renormalisable and unitary, even in higher dimensions and with non-abelian gauge groups. Furthermore, mass terms for gauge bosons and chiral fermions can be generated without spoiling the gauge invariance.

Research paper thumbnail of Monte Carlo Simulations with Complex-Valued Measure

A simulation method based on the RG blocking is shown to yield statistical errors smaller than th... more A simulation method based on the RG blocking is shown to yield statistical errors smaller than that of the crude MC using absolute values of the original measures. The new method is particularly suitable to apply to the sign problem of indefinite or complex-valued measures. We demonstrate the many advantages of this method in the simulation of 2D Ising model with complex-valued temperature.

Research paper thumbnail of Plasmonic tuning of aluminum doped zinc oxide nanostructures by atomic layer deposition

physica status solidi (RRL) - Rapid Research Letters, 2014

Research paper thumbnail of Tackling the Sign Problem

International Journal of Modern Physics C, 1994

To tackle the sign problem in the simulations of systems having indefinite or complex-valued meas... more To tackle the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the original measures. The 1D complex-coupling Ising model is employed as an illustration.

Research paper thumbnail of Measurement in Quantum Physics

International Journal of Modern Physics E, 1999

The conceptual problems in quantum mechanics — related to the collapse of the wave function, the ... more The conceptual problems in quantum mechanics — related to the collapse of the wave function, the particle-wave duality, the meaning of measurement — arise from the need to ascribe particle character to the wave function. As will be shown, all these problems dissolve when working instead with quantum fields, which have both wave and particle character. Otherwise the predictions of quantum physics, including Bell's inequalities, coincide with those of the conventional treatments. The process of decoherence which governs the transfer of the results of the quantum measurement to the classical realm is also carefully discussed.

Research paper thumbnail of On the identification of the ground state based on occupation probabilities: An investigation of Smith's apparent counterexamples

We study a set of truncated matrices, given by Smith~\cite{Smith2005}, in connection to an identi... more We study a set of truncated matrices, given by Smith~\cite{Smith2005}, in connection to an identification criterion for the ground state in our proposed quantum adiabatic algorithm for Hilbert's tenth problem. We identify the origin of the trouble for this truncated example and show that for a suitable choice of some parameter it can always be removed. We also argue that

Research paper thumbnail of Hypercomputability of quantum adiabatic processes: Fact versus Prejudices

We give an overview of a quantum adiabatic algorithm for Hilbert's tenth problem, including s... more We give an overview of a quantum adiabatic algorithm for Hilbert's tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the numerical simulation results of some simple Diophantine equations are presented. We also discuss some prejudicial misunderstandings as well as some plausible difficulties faced by

Research paper thumbnail of Quantum adiabatic algorithm for Hilbert's tenth problem: I. The algorithm

We review the proposal of a quantum algorithm for Hilbert's tenth problem and provide further... more We review the proposal of a quantum algorithm for Hilbert's tenth problem and provide further arguments towards the proof that: (i) the algorithm terminates after a finite time for any input of Diophantine equation; (ii) the final ground state which contains the answer for the Diophantine equation can be identified as the component state having better-than-even probability to be found

Research paper thumbnail of Chiral gauge theory in four dimensions

A formulation of abelian and non-abelian chiral gauge theories is presented together with argumen... more A formulation of abelian and non-abelian chiral gauge theories is presented together with arguments for the unitarity and renormalisability in four dimensions. IASSNS-HEP-94/70, UM-P-94/96, and RCHEP-94/26.

Research paper thumbnail of On the flavour interpretations of staggered fermions

Physics Letters B, 1986

The relatmnship between the flavour identifications of staggered fermions in configuration and m ... more The relatmnship between the flavour identifications of staggered fermions in configuration and m momentum space is clarified for interacting theorms It ~s demonstrated that these ldentlficatmn schemes are identical in the continuum hmlt.

Research paper thumbnail of The Second Law, Maxwell's Demon, and Work Derivable from Quantum Heat Engines

Physical Review Letters, 2004

Research paper thumbnail of Monte Carlo simulation of systems with complex-valued measures

Nuclear Physics B - Proceedings Supplements, 1998

A simulation method based on the RG blocking is shown to yield statistical errors smaller than th... more A simulation method based on the RG blocking is shown to yield statistical errors smaller than that of the crude MC using absolute values of the original measures. The new method is particularly suitable to apply to the sign problem of indefinite or complex-valued measures. We demonstrate the many advantages of this method in the simulation of 2D Ising model with complex-valued temperature.

Research paper thumbnail of More on random-lattice fermions

Nuclear Physics B - Proceedings Supplements, 1995

The lattice fermion determinants, in a given background gauge eld, are evaluated for two dierent ... more The lattice fermion determinants, in a given background gauge eld, are evaluated for two dierent kinds of random lattices and compared to those of naive and wilson fermions in the continuum limit. While the fermion doubling is conrmed on one kind of lattices, there is positive evidence that it may be absent for the other, at least for vector interactions in two dimensions. Combined with previous studies, arbitrary randomness by itself is shown to be not a sucient condition to remove the fermion doublers.

Research paper thumbnail of How do fermions behave on a random lattice?

Nuclear Physics B - Proceedings Supplements, 1993

Comparing random lattice, naive and Wilson fermions in two dimensional abelian background gauge f... more Comparing random lattice, naive and Wilson fermions in two dimensional abelian background gauge field, we show that the doublers suppressed in the free field case are revived for random lattices in the continuum limit unless gauge interactions are implemented in a non-invariant way.

Research paper thumbnail of Mathematical Computability Questions for some Classes of Linear and Non-Linear Differential Equations Originated from Hilbert's Tenth Problem

Computability and Complexity in Analysis, 2005

Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of intege... more Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into problems involving either a set of infinitely-coupled non-linear differential equations or a class of linear Schrodinger equations with some appropriate time- dependent Hamiltonians. We then raise the questions whether these two classes of differential equations are computable or not in some computation models of

Research paper thumbnail of A reformulation of Hilbert's tenth problem through quantum mechanics

Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2004

Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer ar... more Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into either a problem involving a set of infinitely coupled differential equations or a problem involving a Shrödinger propagator with some appropriate kernel. Either way, Mathematics and Physics could be combined for Hilbert's tenth problem and for the notion of effective computability.

Research paper thumbnail of Finite temperature correlations in the Bose-Hubbard model: application of the Gauge <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span> representation

Cornell University - arXiv, Feb 25, 2010

We study ultracold Bose gases in periodic potentials as described by the Bose-Hubbard model. In 1... more We study ultracold Bose gases in periodic potentials as described by the Bose-Hubbard model. In 1D and at finite temperature, we simulate ultracold Bose gases in imaginary time with the gauge P representation. We study various quantities including the Luttinger parameter K, which is important for locating the boundaries of the Mott insulator lobes, and find a simple relation for the kinetic energy part of the Bose-Hubbard Hamiltonian. We show that for J = 0, the stepwise pattern of the average number of particles per lattice site versus the chemical potential vanishes at temperatures above T ≈ 0.1U. Also, at chemical potential µ = 0.5U and temperature T = 0.5U by increasing J, the relative value of the number fluctuation decreases and approaches that of a coherent state.

Research paper thumbnail of Quantum Central Limit Theorems, Emergence of Classicality and Time-dependent Differential Entropy

We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-gr... more We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators. Thanks to the hermicity constraints, we obtain positive-definite distribution for the expectation values of observables. These probability distributions open some pathway for an emergence of classical behaviours in the limit of infinitely large number of identical and non-interacting quantum constituents. This is in contradistinction to other mechanisms of classicality emergence due to environmental decoherence and consistent histories. The probability distributions so derived also enable us to evaluate the nontrivial time-dependence of certain differential entropies.

Research paper thumbnail of A numerical attempt on the chiral Schwinger model

Nuclear Physics B - Proceedings Supplements, 1995

The chiral Schwinger model is formulated in the wilson-fermion formulation on the lattice and the... more The chiral Schwinger model is formulated in the wilson-fermion formulation on the lattice and then simulated by the complex langevin algorithm. The simulation is done both without and with gauge xing to the Lorentz gauge for the compact gauge links. Some preliminary results are presented which indicate that the complex langevin is well behaving with the complex chiral fermion determinant.

Research paper thumbnail of Padé-Z2 stochastic estimator of determinants applied to quark loop expansion of lattice QCD

Nuclear Physics B - Proceedings Supplements, 2001

Research paper thumbnail of What's Wrong with Anomalous Chiral Gauge Theory?

Chinese Journal of Physics- Taipei-

It is argued on general ground and demonstrated in the particular example of the Chiral Schwinger... more It is argued on general ground and demonstrated in the particular example of the Chiral Schwinger Model that there is nothing wrong with apparently anomalous chiral gauge theory. If quantised correctly, there should be no gauge anomaly and chiral gauge theory should be renormalisable and unitary, even in higher dimensions and with non-abelian gauge groups. Furthermore, mass terms for gauge bosons and chiral fermions can be generated without spoiling the gauge invariance.

Research paper thumbnail of Monte Carlo Simulations with Complex-Valued Measure

A simulation method based on the RG blocking is shown to yield statistical errors smaller than th... more A simulation method based on the RG blocking is shown to yield statistical errors smaller than that of the crude MC using absolute values of the original measures. The new method is particularly suitable to apply to the sign problem of indefinite or complex-valued measures. We demonstrate the many advantages of this method in the simulation of 2D Ising model with complex-valued temperature.

Research paper thumbnail of Plasmonic tuning of aluminum doped zinc oxide nanostructures by atomic layer deposition

physica status solidi (RRL) - Rapid Research Letters, 2014

Research paper thumbnail of Tackling the Sign Problem

International Journal of Modern Physics C, 1994

To tackle the sign problem in the simulations of systems having indefinite or complex-valued meas... more To tackle the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the original measures. The 1D complex-coupling Ising model is employed as an illustration.

Research paper thumbnail of Measurement in Quantum Physics

International Journal of Modern Physics E, 1999

The conceptual problems in quantum mechanics — related to the collapse of the wave function, the ... more The conceptual problems in quantum mechanics — related to the collapse of the wave function, the particle-wave duality, the meaning of measurement — arise from the need to ascribe particle character to the wave function. As will be shown, all these problems dissolve when working instead with quantum fields, which have both wave and particle character. Otherwise the predictions of quantum physics, including Bell's inequalities, coincide with those of the conventional treatments. The process of decoherence which governs the transfer of the results of the quantum measurement to the classical realm is also carefully discussed.

Research paper thumbnail of On the identification of the ground state based on occupation probabilities: An investigation of Smith's apparent counterexamples

We study a set of truncated matrices, given by Smith~\cite{Smith2005}, in connection to an identi... more We study a set of truncated matrices, given by Smith~\cite{Smith2005}, in connection to an identification criterion for the ground state in our proposed quantum adiabatic algorithm for Hilbert's tenth problem. We identify the origin of the trouble for this truncated example and show that for a suitable choice of some parameter it can always be removed. We also argue that

Research paper thumbnail of Hypercomputability of quantum adiabatic processes: Fact versus Prejudices

We give an overview of a quantum adiabatic algorithm for Hilbert's tenth problem, including s... more We give an overview of a quantum adiabatic algorithm for Hilbert's tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the numerical simulation results of some simple Diophantine equations are presented. We also discuss some prejudicial misunderstandings as well as some plausible difficulties faced by

Research paper thumbnail of Quantum adiabatic algorithm for Hilbert's tenth problem: I. The algorithm

We review the proposal of a quantum algorithm for Hilbert's tenth problem and provide further... more We review the proposal of a quantum algorithm for Hilbert's tenth problem and provide further arguments towards the proof that: (i) the algorithm terminates after a finite time for any input of Diophantine equation; (ii) the final ground state which contains the answer for the Diophantine equation can be identified as the component state having better-than-even probability to be found

Research paper thumbnail of Chiral gauge theory in four dimensions

A formulation of abelian and non-abelian chiral gauge theories is presented together with argumen... more A formulation of abelian and non-abelian chiral gauge theories is presented together with arguments for the unitarity and renormalisability in four dimensions. IASSNS-HEP-94/70, UM-P-94/96, and RCHEP-94/26.

Research paper thumbnail of On the flavour interpretations of staggered fermions

Physics Letters B, 1986

The relatmnship between the flavour identifications of staggered fermions in configuration and m ... more The relatmnship between the flavour identifications of staggered fermions in configuration and m momentum space is clarified for interacting theorms It ~s demonstrated that these ldentlficatmn schemes are identical in the continuum hmlt.

Research paper thumbnail of The Second Law, Maxwell's Demon, and Work Derivable from Quantum Heat Engines

Physical Review Letters, 2004

Research paper thumbnail of Monte Carlo simulation of systems with complex-valued measures

Nuclear Physics B - Proceedings Supplements, 1998

A simulation method based on the RG blocking is shown to yield statistical errors smaller than th... more A simulation method based on the RG blocking is shown to yield statistical errors smaller than that of the crude MC using absolute values of the original measures. The new method is particularly suitable to apply to the sign problem of indefinite or complex-valued measures. We demonstrate the many advantages of this method in the simulation of 2D Ising model with complex-valued temperature.

Research paper thumbnail of More on random-lattice fermions

Nuclear Physics B - Proceedings Supplements, 1995

The lattice fermion determinants, in a given background gauge eld, are evaluated for two dierent ... more The lattice fermion determinants, in a given background gauge eld, are evaluated for two dierent kinds of random lattices and compared to those of naive and wilson fermions in the continuum limit. While the fermion doubling is conrmed on one kind of lattices, there is positive evidence that it may be absent for the other, at least for vector interactions in two dimensions. Combined with previous studies, arbitrary randomness by itself is shown to be not a sucient condition to remove the fermion doublers.

Research paper thumbnail of How do fermions behave on a random lattice?

Nuclear Physics B - Proceedings Supplements, 1993

Comparing random lattice, naive and Wilson fermions in two dimensional abelian background gauge f... more Comparing random lattice, naive and Wilson fermions in two dimensional abelian background gauge field, we show that the doublers suppressed in the free field case are revived for random lattices in the continuum limit unless gauge interactions are implemented in a non-invariant way.