arXiv subjects

Zachary Lewis

Publications and source records attributed to Zachary Lewis.

12 recordsLinked to original sources

arXiv2026

Architecture Carbon Tool v3: Enabling Sustainability-aware Silicon System Design Exploration

As the carbon cost of manufacturing and operating semiconductor devices has come into sharper focus, sustainability has gradually emerged as a new system architecture design metric. Like power and performance modeling tools, enabling sustainability-aware silicon systems design and optimizations will require a new generation of electronic design automation and architectural modeling tools. Towards this end, we present an update to the Architecture Carbon Tool v3 (ACT3) which aims to provide an extensible and customizable modeling platform for research and advanced development to pave the path towards sustainability-aware architectural design space exploration. Compared to previous versions of ACT, ACT3 provides significantly richer modeling capabilities, enhanced collateral and analysis telemetry, and first order design space exploration capabilities. This technical brief provides an overview of these expanded capabilities and illustrates ACT3's basic utility across several case studies. Finally, we identify opportunities for research and development where we expect the research community can contribute towards continuing to improve sustainability modeling and design methodology for silicon systems.

cs.AR↗

arXiv2015

Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation

We calculate the uncertainties in the position and momentum of a particle in the 1D potential V(x)=F|x|, F>0, when the position and momentum operators obey the deformed commutation relation [x,p]=i\hbar(1+βp^2), β>0. As in the harmonic oscillator case, which was investigated in a previous publication, the Hamiltonian H_1 = p^2/2m + F|x| admits discrete positive energy eigenstates for both positive and negative mass. The uncertainties for the positive mass states behave as Δx ~ 1/Δp as in the β=0 limit. For the negative mass states, however, in contrast to the harmonic oscillator case where we had Δx ~ Δp, both Δx and Δp diverge. We argue that the existence of the negative mass states and the divergence of their uncertainties can be understood by taking the classical limit of the theory. Comparison of our results is made with previous work by Benczik.

hep-th↗

arXiv2014

Quantum F_un: the q=1 Limit of Galois Field Quantum Mechanics, Projective Geometry, and the Field with One Element

We argue that the q=1 limit of Galois Field Quantum Mechanics, which was constructed on a vector space over the Galois Field F_q=GF(q), corresponds to its `classical limit,' where superposition of states is disallowed. The limit preserves the projective geometry nature of the state space, and can be understood as being constructed on an appropriately defined analogue of a `vector' space over the `field with one element' F_1.

quant-ph↗

arXiv2013

Quantum Systems based upon Galois Fields: from Sub-quantum to Super-quantum Correlations

In this talk we describe our recent work on discrete quantum theory based on Galois fields. In particular, we discuss how discrete quantum theory sheds new light on the foundations of quantum theory and we review an explicit model of super-quantum correlations we have constructed in this context. We also discuss the larger questions of the origins and foundations of quantum theory, as well as the relevance of super-quantum theory for the quantum theory of gravity.

quant-ph↗

arXiv2013

Is Quantum Gravity a Super-Quantum Theory?

We argue that quantum gravity should be a super-quantum theory, that is, a theory whose non-local correlations are stronger than those of canonical quantum theory. As a super-quantum theory, quantum gravity should display distinct experimentally observable super-correlations of entangled stringy states.

gr-qc↗

arXiv2013

Biorthogonal Quantum Mechanics: Super-Quantum Correlations and Expectation Values without Definite Probabilities

We propose mutant versions of quantum mechanics constructed on vector spaces over the finite Galois fields GF(3) and GF(9). The mutation we consider here is distinct from what we proposed in previous papers on Galois field quantum mechanics. In this new mutation, the canonical expression for expectation values is retained instead of that for probabilities. In fact, probabilities are indeterminate. Furthermore, it is shown that the mutant quantum mechanics over the finite field GF(9) exhibits super-quantum correlations (i.e. the Bell-Clauser-Horne-Shimony-Holt bound is 4). We comment on the fundamental physical importance of these results in the context of quantum gravity.

math-ph↗

arXiv2013

Spin and Rotations in Galois Field Quantum Mechanics

We discuss the properties of Galois Field Quantum Mechanics constructed on a vector space over the finite Galois field GF(q). In particular, we look at 2-level systems analogous to spin, and discuss how SO(3) rotations could be embodied in such a system. We also consider two-particle `spin' correlations and show that the Clauser-Horne-Shimony-Holt (CHSH) inequality is nonetheless not violated in this model.

quant-ph↗

arXiv2013

Galois Field Quantum Mechanics

We construct a discrete quantum mechanics using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete quantum mechanics cannot be reproduced with any hidden variable theory.

quant-ph↗

arXiv2012

Some Mutant Forms of Quantum Mechanics

We construct a `mutant' form of quantum mechanics on a vector space over the finite Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discretized quantum mechanics cannot be reproduced with any hidden variable theory. An alternative `mutation' is also suggested.

quant-ph↗

arXiv2011

On the Minimal Length Uncertainty Relation and the Foundations of String Theory

We review our work on the minimal length uncertainty relation as suggested by perturbative string theory. We discuss simple phenomenological implications of the minimal length uncertainty relation and then argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy-momentum space. We discuss the implication of this for the problem of vacuum energy and the foundations of non-perturbative string theory.

hep-th↗

arXiv2011

Position and Momentum Uncertainties of the Normal and Inverted Harmonic Oscillators under the Minimal Length Uncertainty Relation

We analyze the position and momentum uncertainties of the energy eigenstates of the harmonic oscillator in the context of a deformed quantum mechanics, namely, that in which the commutator between the position and momentum operators is given by [x,p]=i\hbar(1+βp^2). This deformed commutation relation leads to the minimal length uncertainty relation Δx > (\hbar/2)(1/Δp +βΔp), which implies that Δx ~ 1/Δp at small Δp while Δx ~ Δp at large Δp. We find that the uncertainties of the energy eigenstates of the normal harmonic oscillator (m>0), derived in Ref. [1], only populate the Δx ~ 1/Δp branch. The other branch, Δx ~ Δp, is found to be populated by the energy eigenstates of the `inverted' harmonic oscillator (m<0). The Hilbert space in the 'inverted' case admits an infinite ladder of positive energy eigenstates provided that Δx_{min} = \hbar\sqrtβ > \sqrt{2} [\hbar^2/k|m|]^{1/4}. Correspondence with the classical limit is also discussed.

hep-th↗

arXiv2011

Bell's Inequalities, Superquantum Correlations, and String Theory

We offer an interpretation of super-quantum correlations in terms of a "doubly" quantum theory. We argue that string theory, viewed as a quantum theory with two deformation parameters, the string tension α' and the string coupling constant g_s, is such a super-quantum theory, one that transgresses the usual quantum violations of Bell's inequalities. We also discuss the \hbar\to\infty limit of quantum mechanics in this context. As a super-quantum theory, string theory should display distinct experimentally observable super-correlations of entangled stringy states.

quant-ph↗