Towers of solutions of qKZ equations and their applications to loop models

Cherednik's type A quantum affine Knizhnik-Zamolodchikov (qKZ) equations form a consistent system of linear $q$-difference equations for $V_n$-valued meromorphic functions on a complex $n$-torus, with $V_n$ a module over the GL${}_n$-type extended affine Hecke algebra $\mathcal{H}_n$. The family $(\mathcal{H}_n)_{n\geq 0}$ of extended affine Hecke algebras forms a tower of algebras, with the associated algebra morphisms $\mathcal{H}_n\rightarrow\mathcal{H}_{n+1}$ the Hecke algebra descends of arc insertion at the affine braid group level. In this paper we consider qKZ towers $(f^{(n)})_{n\geq 0}$ of solutions, which consist of twisted-symmetric polynomial solutions $f^{(n)}$ ($n\geq 0$) of the qKZ equations that are compatible with the tower structure on $(\mathcal{H}_n)_{n\geq 0}$. The compatibility is encoded by so-called braid recursion relations: $f^{(n+1)}(z_1,\ldots,z_{n},0)$ is required to coincide up to a quasi-constant factor with the push-forward of $f^{(n)}(z_1,\ldots,z_{n})$ by an intertwiner $\mu_{n}: V_{n}\rightarrow V_{n+1}$ of $\mathcal{H}_{n}$-modules, where $V_{n+1}$ is considered as an $\mathcal{H}_{n}$-module through the tower structure on $(\mathcal{H}_n)_{n\geq 0}$. We associate to the dense loop model on the half-infinite cylinder with nonzero loop weights a qKZ tower $(f^{(n)})_{n\geq 0}$ of solutions. The solutions $f^{(n)}$ are constructed from specialised dual non-symmetric Macdonald polynomials with specialised parameters using the Cherednik-Matsuo correspondence. In the special case that the extended affine Hecke algebra parameter is a third root of unity, $f^{(n)}$ coincides with the (suitably normalized) ground state of the inhomogeneous dense $O(1)$ loop model on the half-infinite cylinder with circumference $n$.Comment: 45 pages. v2: main theorem (Thm. 4.7) strengthened. v3: minor typos corrected. To appear in Ann. Henri Poincar

Nonexistence of Entanglement Sudden Death in High NOON States

We study the dynamics of entanglement in continuous variable quantum systems (CVQS). Specifically, we study the phenomena of Entanglement Sudden Death (ESD) in general two-mode-N-photon states undergoing pure dephasing. We show that for these states, ESD never occurs. These states are generalizations of the so-called High NOON states, shown to decrease the Rayleigh limit of lambda to lambda/N, which promises great improvement in resolution of interference patterns if states with large N are physically realized. However, we show that in dephasing NOON states, the time to reach V_crit, critical visibility, scales inversely with N^2. On the practical level, this shows that as N increases, the visibility degrades much faster, which is likely to be a considerable drawback for any practical application of these states.Comment: 4 pages, 1 figur

Establishing and interpreting international human rights standards : a universal idea in a plural society.

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN023537 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Quantum properties and dynamics of X states

X states are a broad class of two-qubit density matrices that generalize many states of interest in the literature. In this work, we give a comprehensive account of various quantum properties of these states, such as entanglement, negativity, quantum discord and other related quantities. Moreover, we discuss the transformations that preserve their structure both in terms of continuous time evolution and discrete quantum processes.Comment: 13 page

The codes of modesty: reconfiguring the Muslim female subject

This study addresses the relationship between the veil and the constitution of what I have tenned the Muslim female subject in the field of visual and popular culture, with a special emphasis on film. My case-studies range from European historical texts to contemporary visual culture and social practices with reference to the Middle East. The study draws on postcolonial and feminist literature to explore the productions of the Muslim female subject within the discourses of (post)colonialism, nationalism and Islamic patriarchy. It examines the Muslim female subject in relation to the paradigms of veiling and unveiling in a cross-cultural yet context-specific differentiated analysis. The aim is to interrogate the mobility of the veil and the manner in which it can be evaded, substituted or transferred without transgressing the codes of Islamic female modesty. It identifies different manifestations of the veil's mobility, which I contend challenge Islamic hegemonic discourses whilst simultaneously transcending the colonialist paradigm of unveiling. The material I discuss ranges from (de-)colonial cinematic texts, Iranian cinema and advertising for Saudi Arabian Television. I look at canonical texts such as Gillo Pontecorvo's The Battle of Algiers (1966) and Abbas Kiarostami's 10 (2002) in view of their significance in scholarship relating to the Muslim female subject within film studies. I also examine manifestations of the veil in the field of fashion and make extensive reference to paradigmatic representations of the Muslim female subject in contemporary art and curatorial projects

Power straggles and trade in the gulf 1620-1820

Not availabl

Power struggles and trade in the Gulf 1620-1820

Between the death of Nadir Shah, in 1747, and the establishment of the Qajar dynasty in 1795 there were 48 years of Zand rule in Persia, during which time Gulf trade declined and European factories closed down in several ports. Historians have offered varied and insubstantial reasons for this decline. In this thesis an attempt has been made, through the detailed use of primary sources, to offer a more logical and more reasoned interpretation of these developments in place of the older, ill-founded arguments. In our view, the prime cause of the decline in trade and the withdrawal of the trading settlement from Bandar Abbas was the 'commotions', or power struggles in the region. On one hand was the struggle for overall control of Persia whose consequence was the ruin of trade. On the other, the commotion in the area of Bandar Abbas, brought about by MuUa Ali Shah, the Banu Ma in Shaikh, Shaikh Rashid and the Charak Arabs, which was the main cause of the withdrawal from that port. The cessation of trading at Bandar Riq and Khark island was caused by disturbances fomented by Mir Muhanna. According to the English, the main cause of the withdrawal of their settlement from Bandar Rlq was the conflict between Mir Muhanna and Karim Khan about Bandar Riq. But it was Mir Muhanna's suspicion that the English were his enemies and that they were the allies of Karim Khan which caused their expulsion. The Dutch, for their part, were expelled from Khark island after they had joined forces with Bushire in attacking Mir Muhanna on the orders of Karim Khan. In Bushire the case was different. Although the English acted neutrally in the conflicts they could not evade the dangers. They had suffered losses at Mir Muhanna's hands but Karim Khan believed that the English were refusing to help him against the Mir. The anger of Karim Khan, his determination not to receive the English in audience, and the fear that his brother, Zald Khan, would detain the English Agent in Bushire all motivated the withdrawal of the English settlement from there. At last, when the Qajar dynasty took control of all the Persian provinces at the beginning of the 19th century, the value of English trade with Persia increased enormously

Do all states undergo sudden death of entanglement at finite temperature?

In this paper we consider the decay of quantum entanglement, quantified by the concurrence, of a pair of two-level systems each of which is interacting with a reservoir at finite temperature T. For a broad class of initially entangled states, we demonstrate that the system always becomes disentangled in a finite time i.e."entanglement sudden death" (ESD) occurs. This class includes all states which previously had been found to have long-lived entanglement in zero temperature reservoirs. Our general result is illustrated by an example.Comment: 4 pages, 3 figure