A time-dependent variational principle for dissipative dynamics

We extend the time-dependent variational principle to the setting of dissipative dynamics. This provides a locally optimal (in time) approximation to the dynamics of any Lindblad equation within a given variational manifold of mixed states. In contrast to the pure-state setting there is no canonical information geometry for mixed states and this leads to a family of possible trajectories --- one for each information metric. We focus on the case of the operationally motivated family of monotone riemannian metrics and show further, that in the particular case where the variational manifold is given by the set of fermionic gaussian states all of these possible trajectories coincide. We illustrate our results in the case of the Hubbard model subject to spin decoherence.Comment: Published versio

Ground States of Fermionic lattice Hamiltonians with Permutation Symmetry

We study the ground states of lattice Hamiltonians that are invariant under permutations, in the limit where the number of lattice sites, N -> \infty. For spin systems, these are product states, a fact that follows directly from the quantum de Finetti theorem. For fermionic systems, however, the problem is very different, since mode operators acting on different sites do not commute, but anti-commute. We construct a family of fermionic states, \cal{F}, from which such ground states can be easily computed. They are characterized by few parameters whose number only depends on M, the number of modes per lattice site. We also give an explicit construction for M=1,2. In the first case, \cal{F} is contained in the set of Gaussian states, whereas in the second it is not. Inspired by that constructions, we build a set of fermionic variational wave functions, and apply it to the Fermi-Hubbard model in two spatial dimensions, obtaining results that go beyond the generalized Hartree-Fock theory.Comment: 23 pages, published versio

The \u3cem\u3eInsular Cases\u3c/em\u3e Run Amok: Against Constitutional Exceptionalism in the Territories

The Insular Cases have been enjoying an improbable — and unfortunate — renaissance. Decided at the height of what has been called the “imperialist” period in U.S. history, this series of Supreme Court decisions handed down in the early twentieth century infamously held that the former Spanish colonies annexed by the United States in 1898 — Puerto Rico, the Philippines, and Guam — “belong[ed] to, but [were] not a part of, the United States.” What exactly this meant has been the subject of considerable debate even as those decisions have received unanimous condemnation. According to the standard account, the Insular Cases held that the “entire” Constitution applies within the United States (defined as the states, the District of Columbia, and the so-called “incorporated” territories) while only its “fundamental” limitations apply in what came to be known as the “unincorporated” territories (today, Puerto Rico, Guam, the U.S. Virgin Islands, the Northern Mariana Islands, and American Samoa). Scholars unanimously agree that the Insular Cases gave the Court’s sanction to U.S. colonial rule over the unincorporated territories — and that the reason for it was racism. Yet courts and scholars have recently sought to hoist the Insular Cases on their own racist petard — by “repurposing” them to defuse constitutional objections to certain distinctive cultural practices in the unincorporated territories. Adopting the standard account of the Insular Cases, according to which they created a nearly extraconstitutional zone, proponents of repurposing argue that the relative freedom from constitutional constraints that government action enjoys in the unincorporated territories can and should be exploited now to vindicate their peoples’ right to cultural self-preservation. This Article disagrees. Although I share the view that the Constitution should not ride roughshod over the cultural practices of the people of the unincorporated territories, I do not agree that the Constitution necessarily must bend to any such practices it finds there or that the Insular Cases present a legitimate — let alone desirable — doctrinal vehicle for preserving such practices. Instead, constitutional doctrines available outside of the Insular Cases present the most promising — and the only legitimate — doctrinal means for making the constitutional case in favor of cultural accommodation. Against the repurposing project, I argue that the Insular Cases gave rise to nothing less than a crisis of political legitimacy in the unincorporated territories, and that no amount of repurposing, no matter how well-intentioned — or even successful — can change that fact. On the contrary: repurposing the Insular Cases will prolong the crisis. They should be overruled

Love and War

Legal historians: Find a window to read Rose Cuison Villazor’s “The Other Loving,” published in the NYU Law Review last fall. Although Villazor, Associate Professor of Law at Hofstra, does not identify primarily as a legal historian, she has written more than one historical work well worth a read. An earlier article examined alien land laws in the United States, telling the story of Oyama v. California (1948), which held unconstitutional a provision of California’s Alien Land Law that discriminated against owners of property bought by parents who were ineligible to become U.S. citizens. This more recent article, in turn, explores how immigration, citizenship, and military statutes and regulations in the period around World War II interacted to produce federal anti-miscegenation law, with both domestic and extraterritorial effects. Carefully researched and engagingly written, Villazor’s article seeks to challenge the conventional view that legal restrictions on marriage have traditionally been the sole domain of state, not federal, law – with implications for historical scholarship and for current political debates

They say I am not an American… : The Noncitizen National and the Law of American Empire

The American papers sometimes contain tales about persons who have forgotten who they are, what are their names, and where they live. The Porto [sic] Ricans find themselves in the same predicament as those absent-minded people. To what nationality do they belong? What is the character of their citizenship? ... [l]f since they ceased to be Spanish citizens they have not been Americans [sic] citizens, what in the name ·of heaven have they been

To Enumerate or Not to Enumerate: A Theory of Congressional Great Powers

I have a soft spot for any argument that tends to show the relevance of long-settled constitutional controversies over territorial annexation to hotly debated current events. Even so, I wouldn’t write about this piece if I didn’t think it was well worth reading regardless of how much one cares about the United States’ imperial adventures of over a century ago – or about any given headline today, for that matter