From University of Cambridge (UK) : “‘Back to basics’ approach helps unravel new phase of matter”

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From University of Cambridge (UK)

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A new phase of matter, thought to be understandable only using quantum physics, can be studied with far simpler classical methods.

Researchers from the University of Cambridge used computer modelling to study potential new phases of matter known as prethermal discrete time crystals (DTCs). It was thought that the properties of prethermal DTCs were reliant on quantum physics: the strange laws ruling particles at the subatomic scale. However, the researchers found that a simpler approach, based on classical physics, can be used to understand these mysterious phenomena.

Understanding these new phases of matter is a step forward towards the control of complex many-body systems, a long-standing goal with various potential applications, such as simulations of complex quantum networks. The results are reported in two joint papers in Physical Review Letters and Physical Review B.

When we discover something new, whether it’s a planet, an animal, or a disease, we can learn more about it by looking at it more and more closely. Simpler theories are tried first, and if they don’t work, more complicated theories or methods are attempted.

“This was what we thought was the case with prethermal DTCs,” said Andrea Pizzi, a PhD candidate in Cambridge’s Cavendish Laboratory, first author on both papers. “We thought they were fundamentally quantum phenomena, but it turns out a simpler classical approach let us learn more about them.”

DTCs are highly complex physical systems, and there is still much to learn about their unusual properties. Like how a standard space crystal breaks space-translational symmetry because its structure isn’t the same everywhere in space, DTCs break a distinct time-translational symmetry because, when ‘shaken’ periodically, their structure changes at every ‘push’.

“You can think of it like a parent pushing a child on a swing on a playground,” said Pizzi. “Normally, the parent pushes the child, the child will swing back, and the parent then pushes them again. In physics, this is a rather simple system. But if multiple swings were on that same playground, and if children on them were holding hands with one another, then the system would become much more complex, and far more interesting and less obvious behaviours could emerge. A prethermal DTC is one such behaviour, in which the atoms, acting sort of like swings, only ‘come back’ every second or third push, for example.”

First predicted in 2012, DTCs have opened a new field of research, and have been studied in various types, including in experiments. Among these, prethermal DTCs are relatively simple-to-realise systems that don’t heat quickly as would normally be expected, but instead exhibit time-crystalline behaviour for a very long time: the quicker they are shaken, the longer they survive. However, it was thought that they rely on quantum phenomena.

“Developing quantum theories is complicated, and even when you manage it, your simulation capabilities are usually very limited, because the required computational power is incredibly large,” said Pizzi.

Now, Pizzi and his co-authors have found that for prethermal DTCs they can avoid using overly complicated quantum approaches and use much more affordable classical ones instead. This way, the researchers can simulate these phenomena in a much more comprehensive way. For instance, they can now simulate many more elementary constituents, getting access to the scenarios that are the most relevant to experiments, such as in two and three dimensions.

Using a computer simulation, the researchers studied many interacting spins – like the children on the swings – under the action of a periodic magnetic field – like the parent pushing the swing – using classical Hamiltonian dynamics. The resulting dynamics showed in a neat and clear way the properties of prethermal DTCs: for a long time, the magnetisation of the system oscillates with a period larger than that of the drive.

“It’s surprising how clean this method is,” said Pizzi. “Because it allows us to look at larger systems, it makes very clear what’s going on. Unlike when we’re using quantum methods, we don’t have to fight with this system to study it. We hope this research will establish classical Hamiltonian dynamics as a suitable approach to large-scale simulations of complex many-body systems and open new avenues in the study of nonequilibrium phenomena, of which prethermal DTCs are just one example.”

Pizzi’s co-authors on the two papers, who were both recently based at Cambridge, are Dr Andreas Nunnenkamp, now at The University of Vienna [Universität Wien] (AT), and Dr Johannes Knolle, now at The Technical University of Munich [Technische Universität München] (DE).

Meanwhile, at UC Berkeley, Norman Yao’s group has also been using classical methods to study prethermal DTCs. Remarkably, the Berkeley and Cambridge teams have simultaneously addressed the same question. Yao’s group will be publishing their results shortly.

Science papers:

Physical Review Letters

Physical Review B

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The University of Cambridge (UK) [legally The Chancellor, Masters, and Scholars of the University of Cambridge] is a collegiate public research university in Cambridge, England. Founded in 1209 Cambridge is the second-oldest university in the English-speaking world and the world’s fourth-oldest surviving university. It grew out of an association of scholars who left the University of Oxford(UK) after a dispute with townsfolk. The two ancient universities share many common features and are often jointly referred to as “Oxbridge”.

Cambridge is formed from a variety of institutions which include 31 semi-autonomous constituent colleges and over 150 academic departments, faculties and other institutions organised into six schools. All the colleges are self-governing institutions within the university, each controlling its own membership and with its own internal structure and activities. All students are members of a college. Cambridge does not have a main campus and its colleges and central facilities are scattered throughout the city. Undergraduate teaching at Cambridge is organised around weekly small-group supervisions in the colleges – a feature unique to the Oxbridge system. These are complemented by classes, lectures, seminars, laboratory work and occasionally further supervisions provided by the central university faculties and departments. Postgraduate teaching is provided predominantly centrally.

Cambridge University Press a department of the university is the oldest university press in the world and currently the second largest university press in the world. Cambridge Assessment also a department of the university is one of the world’s leading examining bodies and provides assessment to over eight million learners globally every year. The university also operates eight cultural and scientific museums, including the Fitzwilliam Museum, as well as a botanic garden. Cambridge’s libraries – of which there are 116 – hold a total of around 16 million books, around nine million of which are in Cambridge University Library, a legal deposit library. The university is home to – but independent of – the Cambridge Union – the world’s oldest debating society. The university is closely linked to the development of the high-tech business cluster known as “Silicon Fe”. It is the central member of Cambridge University Health Partners, an academic health science centre based around the Cambridge Biomedical Campus.

By both endowment size and consolidated assets Cambridge is the wealthiest university in the United Kingdom. In the fiscal year ending 31 July 2019, the central university – excluding colleges – had a total income of £2.192 billion of which £592.4 million was from research grants and contracts. At the end of the same financial year the central university and colleges together possessed a combined endowment of over £7.1 billion and overall consolidated net assets (excluding “immaterial” historical assets) of over £12.5 billion. It is a member of numerous associations and forms part of the ‘golden triangle’ of English universities.

Cambridge has educated many notable alumni including eminent mathematicians; scientists; politicians; lawyers; philosophers; writers; actors; monarchs and other heads of state. As of October 2020 121 Nobel laureates; 11 Fields Medalists; 7 Turing Award winners; and 14 British prime ministers have been affiliated with Cambridge as students; alumni; faculty or research staff. University alumni have won 194 Olympic medals.

History

By the late 12th century the Cambridge area already had a scholarly and ecclesiastical reputation due to monks from the nearby bishopric church of Ely. However it was an incident at Oxford which is most likely to have led to the establishment of the university: three Oxford scholars were hanged by the town authorities for the death of a woman without consulting the ecclesiastical authorities who would normally take precedence (and pardon the scholars) in such a case; but were at that time in conflict with King John. Fearing more violence from the townsfolk scholars from the University of Oxford started to move away to cities such as Paris; Reading; and Cambridge. Subsequently enough scholars remained in Cambridge to form the nucleus of a new university when it had become safe enough for academia to resume at Oxford. In order to claim precedence it is common for Cambridge to trace its founding to the 1231 charter from Henry III granting it the right to discipline its own members (ius non-trahi extra) and an exemption from some taxes; Oxford was not granted similar rights until 1248.

A bull in 1233 from Pope Gregory IX gave graduates from Cambridge the right to teach “everywhere in Christendom”. After Cambridge was described as a studium generale in a letter from Pope Nicholas IV in 1290 and confirmed as such in a bull by Pope John XXII in 1318 it became common for researchers from other European medieval universities to visit Cambridge to study or to give lecture courses.

Foundation of the colleges

The colleges at the University of Cambridge were originally an incidental feature of the system. No college is as old as the university itself. The colleges were endowed fellowships of scholars. There were also institutions without endowments called hostels. The hostels were gradually absorbed by the colleges over the centuries; but they have left some traces, such as the name of Garret Hostel Lane.

Hugh Balsham, Bishop of Ely, founded Peterhouse – Cambridge’s first college in 1284. Many colleges were founded during the 14th and 15th centuries but colleges continued to be established until modern times. There was a gap of 204 years between the founding of Sidney Sussex in 1596 and that of Downing in 1800. The most recently established college is Robinson built in the late 1970s. However Homerton College only achieved full university college status in March 2010 making it the newest full college (it was previously an “Approved Society” affiliated with the university).

In medieval times many colleges were founded so that their members would pray for the souls of the founders and were often associated with chapels or abbeys. The colleges’ focus changed in 1536 with the Dissolution of the Monasteries. Henry VIII ordered the university to disband its Faculty of Canon Law and to stop teaching “scholastic philosophy”. In response, colleges changed their curricula away from canon law and towards the classics; the Bible; and mathematics.

Nearly a century later the university was at the centre of a Protestant schism. Many nobles, intellectuals and even commoners saw the ways of the Church of England as too similar to the Catholic Church and felt that it was used by the Crown to usurp the rightful powers of the counties. East Anglia was the centre of what became the Puritan movement. In Cambridge the movement was particularly strong at Emmanuel; St Catharine’s Hall; Sidney Sussex; and Christ’s College. They produced many “non-conformist” graduates who, greatly influenced by social position or preaching left for New England and especially the Massachusetts Bay Colony during the Great Migration decade of the 1630s. Oliver Cromwell, Parliamentary commander during the English Civil War and head of the English Commonwealth (1649–1660), attended Sidney Sussex.

Modern period

After the Cambridge University Act formalised the organisational structure of the university the study of many new subjects was introduced e.g. theology, history and modern languages. Resources necessary for new courses in the arts architecture and archaeology were donated by Viscount Fitzwilliam of Trinity College who also founded the Fitzwilliam Museum. In 1847 Prince Albert was elected Chancellor of the University of Cambridge after a close contest with the Earl of Powis. Albert used his position as Chancellor to campaign successfully for reformed and more modern university curricula, expanding the subjects taught beyond the traditional mathematics and classics to include modern history and the natural sciences. Between 1896 and 1902 Downing College sold part of its land to build the Downing Site with new scientific laboratories for anatomy, genetics, and Earth sciences. During the same period the New Museums Site was erected including the Cavendish Laboratory which has since moved to the West Cambridge Site and other departments for chemistry and medicine.

The University of Cambridge began to award PhD degrees in the first third of the 20th century. The first Cambridge PhD in mathematics was awarded in 1924.

In the First World War 13,878 members of the university served and 2,470 were killed. Teaching and the fees it earned came almost to a stop and severe financial difficulties followed. As a consequence the university first received systematic state support in 1919 and a Royal Commission appointed in 1920 recommended that the university (but not the colleges) should receive an annual grant. Following the Second World War the university saw a rapid expansion of student numbers and available places; this was partly due to the success and popularity gained by many Cambridge scientists.